DIRECT ECONOMIC EFFECTS OF INCREASED ENERGY PRICES ON OPTIMAL CORN AND SOYBEAN PRODUCTION ON CASH DRAIN FARMS IN SOUTHEASTERN MICHIGAN Thesis for the Degree Of M. S. MICHIGAN STATE UNIVERSITY JAMES ALLEN LEHRMANN 1976 IIIIIIIIIIIIIIIIIIIIIIIIIIIIII“TIMIIIIIIIIIIIIIIIIII I 3 1293 104 61 6 This is to certify that the thesis entitled Direct Economic Effects of Increased Energy Prices on Corn and Soybean Production on Southeastern Michigan Cash Grain Farms presented by James Allen Lehrmann has been accepted towards fulfillment of the requirements for M.S. degree”, Agric. Econ. , C «2x (B 2 / or professor Date ApriT 15, 1976 0-7639 ‘L' DIRECT ECO!I OPTIMAL COE AS agr And use of 1; has increase; become less 5 in“ Producti other rESearc SUCtion has i increaSEd ene ically apPrOp _ The sub has caused uh ABSTRACT DIRECT ECONOMIC EFFECTS OF INCREASED ENERGY PRICES ON OPTIMAL CORN AND SOYBEAN PRODUCTION ON CASH GRAIN FARMS IN SOUTHEASTERN MICHIGAN BY James Allen Lehrmann As agricultural production has become more mechanized and use of land substitutes such as commercial fertilizers has increased, some researchers claim that agriculture has become less energy efficient. The ratio of energy inputs into production to energy derived from outputs has increased. Other researchers contend that the economic return to pro- duction has increased as energy inputs have grown, making increased energy use in agricultural production an econom-I ically appropriate step. The substantial increase in energy prices since 1973 has caused the costs of corn and soybean production to increase. Because soybeans are less energy intensive than corn, the relative profitability of soybeans to corn has increased. The objectives of this study were (1) to deter- ndne the optimal crop mix that maximizes profit of a cash grain farm in Southeastern Michigan under present conditions, under 1 prices; should and (3) corn anc Tc linear p internal grain fa] include f zhachil'zery labor aVa Vities CO] soybean h} fall Peric the effect soybe‘mtco (3) p001. We Anal) i319 genEral l. p hi‘brids Pla; near maXimur fie Soybean: CIGaSeS’ Q. “D Ort S ~ James Allen Lehrmann under increasing energy prices, and under increasing soybean prices; (2) to discuss what adjustments, if any, farmers should make to conform with the profit maximizing crop mix; and (3) to discuss the implications of optimal behavior on ' corn and soybean supply reSponse. To determine the optimal corn and soybean mix, a linear programming model was developed incorporationg the internal and external characteristics of a "typical" cash grain farm in Southeastern Michigan. These characteristics include factors such as land availability, soil type, machinery supply, potential crop yields, weather conditions, labor availability, and prices. Potential production acti- vities consist of short, medium, and long season corn and soybean hybrids planted and harvested in various spring and fall periods. Sensitivity analysis was used to determine the effects on optimal crop mix caused by (1) increasing soybeanzcorn price ratio, (2) increasing energy prices, and (3) poor weather conditions. Analysis of the sensitivity results led to the follow- ing general condlusions: l. Profits are maximized by growing long season corn hybrids planted in early Spring periods and harvested at near maximum yield levels and short season soybeans. As the soybean:corn price ratio increases, corn acreage de- creases, operating income increases, and energy use declines. Short season corn hybrids have limited use because their potential yield levels are low relative to other corn hybrids. 2. mix as co relating I condition: is equival determine increase b price incr. 3. I' Short-run 5 decrease, corn and so Demflllatio eluilibrium James Allen Lehrmann 2. The farmer should determine how to adjust his cr0p mix as corn and soybean prices change by using a simple model relating machinery capacity, potential yield, and weather conditions on his farm. Because an increase in energy prices is equivalent to an increase in soybean price, the farmer can determine how to change his crOp mix When energy prices increase by translating the energy increase into a soybean price increase. 3. A significant increase in energy prices causes short-run soybean supplies to increase and corn supplies to decrease. Long-run equilibrium of aggregate supplies of corn and soybeans is less than previous equilibrium levels. Deregulations of energy prices would cause the long-run equilibrium prices of corn and soybeans to increase by $0.12 and $0.04 per bushel, respectively. 4. Deregulation of energy prices has a relatively minor effect on corn and soybean production. A govern- mental policy to reduce energy use in agriculture by deregu- lating prices would do little to reduce consumption. 5. Increasing energy efficiency by using short season corn hybrids and increased field drying causes net farm profit to decrease by 15-20 percent. DIRECT EC OPTIMAL C 1“ Pa: DIRECT ECONOMIC EFFECTS OF INCREASED ENERGY PRICES ON OPTIMAL CORN AND SOYBEAN PRODUCTION ON CASH GRAIN FARMS IN SOUTHEASTERN MICHIGAN BY James Allen Lehrmann A THESIS Submitted to Michigan State University in partial fulfillment of requirements for the degree of MASTER OF SCIENCE Department of Agricultural Economics 1976 In memory of Rueben H. Lehrmann ii The a: Connor for 5 dance. conce rent of the ACKNOWLEDGMENTS The author would like to especially thank Dr. Larry Connor for serving so well as a major professor. His gui- dance, concern, and constructive criticisms made the achieve- ment of the author's academic goals much easier. Appreciation is also given to Dr. J. Roy Black for his work as thesis supervisor. His direction made this project an enjoyable as well as an educational experience. Thanks should be given to Dr. B. A. Stout for his helpful comments and to Dr. Steve Harsh for his help in developing the LP model. Other individuals provided infor- mation and advice that was greatly appreciated. Appreciation should be extended to the Agricultural Economics Department and the Experiment Station for the facilities and financial support granted. Finally, a special thanks should be extended to my family and to the numerous friends who have made the stay here at Michigan State the most rewarding and enjoyable experience of this.life. iii Chapte r I. II. III. IV. Chapter I. II. III. IV. TABLE OF CONTENTS INTRODUCTION 0 O O O O C O O O O O O 0 Problem Setting . . . . . . . . . . Objectives . . . . . . . . . . . . Procedure . . . . . . . . . . . . . REVIEW OF SUPPLY RESPONSE THEORY . . . Short-Run Farm Production Response Aggregate Supply Response . . . . . Effects on Livestock Supplies and Prices 0 O O O O O O O O O O O O 0 DEVELOPMENT OF A DECISION MODEL . . . Purpose of Model Development . . . Assumptions and Description of Typical Farm . . . . . . . . . . . Sources of In ormation . . . Structure of the LP Model . . . . . Data Calculations . . . . . . . . . MODEL RESULTS UNDER PRESENT CONDITIONS Explanation of Model Results . . . Model Results Under Present Conditions. Effect of Requiring Low Moisture Corn ActiVities O O O O O I O O O O O 0 DEVELOPMENT AND RESULTS OF SENSITIVITY ANALYSES O O I I O O O O O O O O C O 0 Purpose of Sensitivity Analysis . . Analysis Procedure . . . . . . . . Pricing Assumptions . . . . . . . . Price Ranges for Each Analysis . . Results of Sensitivity Analyses . . Comparison of Results with Real Wor Changes . . . . . . . . . . . . . . iv Page m~4 I4 U1b+e H 13 16 16 17 20 26 38 38 39 41 44 44 45 49 53 59 Chapter VI . APPENDICES Chapter VI. CONCLUSIONS AND IMPLICATIONS OF MODEL RESULTS 0 O O C I O O O O O O C O C O O APPENDICES A . . . . B O O 'O O BIBLIOGRAPHY Problem Review . . . . . . . . . . . Review of Model Results . . . . . . Implications on Farm Adjustments . . Effects of Energy Price Increases on Supply Responses . . . . . . . . . Review of Significant Conclusions . Limitations of This Study . . . . . Additional Useful Research . . . . . Page 62 62 63 65 67’ 69 72 74 75 93 117 Table A1. A2. A3. A4. A5, A7, A9, LIST OF TABLES Table Page 1. Expected Yield and Moisture Contents of Corn. 21 2.. Expected Soybean Yields . . . . . . . . . . . 22 3. Acreage and Income Effects of Corn and Soybean Price Changes . . . . . . . . . . . . . . . . 54 4. Acreage and Income Effects of Natural Gas Price Increases . . . . . . . . . . . . . . . SS 5. Acreage and Income Effects of Crude Oil Price Increases . . . . . . . . . . . . . . . 56 6. Acreage and Income Effects of Simultaneous Oil and Gas Price Increases . . . . . . . . . 57 7. Acreage and Income Effects of Limited Spring Planting O C O O O O O O O O O O I O O I O O 59 8. Changes in Percentage Corn Acreage as PriCe Ratios Change . . . . . . . . . . . . . . . . 60 Al. Corn and Soybean Activity Information . . . . 79 A2. Resource Constraints . . . . . . . . . . . . 85 A3. Time Available for Field Work by Calendar Period for Well Drained Soils . . . . . . . . 86 A4. Variable Costs . . . . . . . . . . . . . . . 87 A5. Total Variable Costs . . . . . . . . . . . . 88 A6. Diesel Use . . . . . . . . . . . . . . . . . 89 A7. Average Environmental Conditions, Southern Michigan . . . . . . . . . . . . . . . . . . 90 A8. Input and Product Prices . . . . . . . . . . 91 A9. Annual Fixed Costs of Typical Farm . . . . . 92 vi Table 81. 82. B3. B4. B6. rn Table Page Bl. Input Costs of Anhydrous Ammonia . . . . . . 94 82. Input Costs of Ammonium Nitrate . . . . . . 95 B3. Objectives of Various Sensitivity Analyses . 96 B4. Inputs, Outputs, and Unit Prices of the Sensitivity Analyses . . . . . . . . . . . . 97 B5. Activities and Constraints of the Sensi- tivity Analyses . . . . . . . . . . . . . . 103 B6. Listing of Specific Activities in Optimal SOlution O O I O O O O O O O I O O O I O O O 115 vii Figure Exhibi t Al. 31. Re PC LE> Fi Vex E)ga Inc Figure 1. Exhibit A1. A2. Bl. LIST OF FIGURES Effect of Increased Energy Prices on Enterprise Combinations . . . . . . . . . . Industry Supply Responses Caused by Energy Price Increases . . . . . . . . . . . . . . Revised Cobweb with Supply Curve Adjustment Potential Adjustments in Livestock Feeding. LP Tableau . . . . . . . . . . . . . . . . Field Operations Flow Chart . . . . . . . . LIST OF EXHIBITS Verbal Description of LP Model Structure . . Example of Equivalence of Soybean Price Increase and an Energy Price Increase . . . Sample Calculation of Energy Price Variation. viii Page 10 12 14 24 25 Page 75 77 93 Americ efficient in eight other ; efficiency ha CHAPTER I INTRODUCTION Problem Setting American agriculture has been proclaimed as the most efficient in the world. One farmer provides food for forty- eight other people [4]*. One major reason for this improved efficiency has been the substitution of fertilizers, pesticides, new hybrids, and improved cultural practices for land. Another cause of this high labor productivity is a substantial capital investment in farm machinery and equipment. Energy using machinery and inputs have replaced labor. The energy needed for these inputs is provided primarily by fossil fuels such as crude oil and natural gas. The prudence of high energy input use in agriculture has been questioned by numerous researchers. Pimentel [4] and Heichel [2] investigated the ratio of energy inputted into production of various crops to the amount of energy available for the harvested crop. This analysis procedure is known as energy accounting. For corn grain, Pimentel estimated one calorie of input produced 2.82 calories of output. Heichel's ratio for corn is 4.40. Perelman [3] and Steinhart and Steinhart [5] suggest that if total energy input into the *Refers to number of reference at the end of the chapter. food system tation, pro than produc of input we- These resea- agriculture to be made t But se used to anal problem of f, IS a calorie Energy in CO: ”hiCh reflec: that a relat: this equating outPuts, 1.9. in the Variou lihg the C810 be made. A.IlOther non of SUPPII lite USeg 0f I -c Us natural ga‘ he Supply of 10. . Te Efficient Ding charaC food system, including farm machinery manufacturing, transpor- tation, processing, etc. is considered, more energy is used than produced. Steinhart and Steinhart show that 9 calories of input were required to get one calorie of output in 1970. These researchers have drawn the conclusion that American agriculture is not energy efficient and that adjustments have to be made to reduce energy use. But several problems arise when energy accounting is used to analyze production techniques. First, there is the problem of finding a common denominator for the analysis. Is a calorie of energy in manure equivalent to a calorie of energy in corn? Sources of energy must be equated in a manner which reflects their "usefulness" to humans. If it is assumed that a relatively competitive market is present, one proxy for this equating process is monetary pricing of energy inputs and outputs, i.e., dollars. If the cost of the calories contained in the various inputs exceeds the revenue generated from sel- ling the calories of output, adjustments in energy use should be made. Another problem of energy accounting is the nonrecogni- tion of supply levels of various energy sources and the ulti- mate uses of various energy sources. For instance, a calorie of natural gas is more precious than a calorie of coal because the supply of natural gas is smaller, transporting gas is more efficient, and consumers demand natural gas for its clean burning characteristics and ease of handling. Likewise, natural gas energy 1 the energy i more valuabl relative val Energy rorcomplemen developed to particularly in nitrogen N “Ch as fert: substitutes f be able to pr Ptts COUld pr The ene efficiency in use. BY far, gas energy is more readily usable for various purposes than the energy in manure, again causing natural gas to be relatively more valuable.‘ Prices in a free competitive market refleCt the relative value of various energy sources. Energy accounting does not recognize the substitutability norcomplementarity of agricultural inputs. Corn hybrids were developed to be used with high levels of commercial fertilizers, particularly nitrogen. Reduction of the energy input inherent in nitrogen will also reduce corn yields. Energy related inputs such as fertilizers, pesticides, drainage, and irrigation are substitutes for land. One acre of land using these inputs might be able to produce what three acres of land without these in- puts could produce. The energy accounting procedure used to estimate energy efficiency in agriculture does not account for solar energy use. By far, the largest energy input into cr0p production is solar energy. If energy input includes solar energy, pro- duction systems using inputs such as fertilizer, pesticides, etc. on smaller acreages use less energy than larger tracts without the benefit of land substitutes. Of course, economic accounting using dollars as the common denominator is not a perfect solution. Institutional restraints such as price controls may cause improper balancing' of energy use. Also, dollar pricing may not allocate future supplies of energy sources properly. But economic accounting of energy use is a more appropriate means of evaluating pro- per energy use in agriculture than energy accounting. Since ture has in in agricult“ cost increas by keeping e Wwer units that CIOppinC Preportion 0: “Port [1] 5; improved dry 1 grain use COu But such adj u Profitability On a mo; an individUal yiehigan make or increasing 3:”! individua DDthe aggreg craps and the “we“ to th 53?“ 1 Since 1973 the price of many energy inputs of agricul- ture has increased significantly. What economic adjustments in agricultural production techniques do these significant cost increases make necessary? Fuel costs can be minimized by keeping engines properly tuned and by correctly matching power units and equipment to the job. Pimentel [4] indicates that cropping systems should be changed to include a greater proportion of crops that are more energy efficient. The CAST report [1] suggests that a switch to all diesel power units, improved drying techniques and procedures, and high moisture grain use could reduce energy requirements of agriculture. But such adjustments will occur only if they increase the profitability of the farm. On a more specific basis, what adjustments, if any, should an individual operator of a cash grain farm in Southeastern Michigan make to improve energy efficiency while maintaining or increasing profitability? What are the probable effects of any individual farm adjustments in corn and soybean production on the aggregate supplies and equilibrium prices of these crops and the livestock enterprises they support? Finding answers to these questions could be of great importance to agriculture and the national economy. Objectives The purpose of this study was to investigate and answer the two questions directly above. More specifically, the objectives of this research were: (2) (l) to determine the optimal crOp mix and scheduling plan that maximizes the profitability of a cash grain farm in Southeastern Michigan caused by (a) changes in energy prices, (b) changes in relative prices of corn and soybeans, and (c) unfavorable weather conditions; (2) to discuss the adjustments that a farm manager should make in crop mix and scheduling plans given (a) changes in energy priCes, (b) changes in relative prices of corn and soybeans, and (c) unfavorable weather conditions; (3) to discuss the potential effects on corn and soybean supplies and prices caused by increasing energy prices. Procedure The remainder of this thesis is organized in the follow- ing manner. In Chapter II a brief review of supply theory is presented. Chapter III is an explanation of the derivation of the linear programming model, the assumptions uSed, its structure, and the data calculations. In Chapter IV the results of the model under present conditions are given. The results of the various sensitivity analyses of the model are contained in Chapter V. And in Chapter VI a discussion of conclusions and implications concerning the objectives and limitations of the study is given. H] [N Pereln 14:8-1 Piment Crisis Stein} Use it 1974. [1] [2] [31 [4] [5] REFERENCES Council for Agricultural Science and Technology, Po- tential for Energy_Conservation in Agricultural Pro- duction, Report No. 40, February 6, 1975. Heichel, G. H., Comparative Efficiency of Energy Use in CrOp Production, The Connecticut Agricultural Experiment Station, New Haven, Bulletin 739, 1973. Perelman, M. J., "Farming with Petroleum," Environment, 14:8-13, 1972. Pimentel, D., et al., "Food Production and the Energy Crisis," Science, 182:443-449, 1973. Steinhart, John S. and Steinhart, Carol E., "Energy Use in U.S. Agriculture," Science, 184:307-316, April, 1974. rn One of implications s“Pplies of I understand hg Costs 0f proc this Chapter to make Corre In“ SW TIT Change AS energ 519318: prOduC CHAPTER II REVIEW OF SUPPLY RESPONSE THEORY Short-Run Farm Production Responses One of the objectives of this thesis is to discuss the implications of increased energy prices on the aggregate supplies of corn and soybeans. Therefore, it is important to understand how total supplies of these products change as costs of production and product prices change. The purpose of this chapter is to present the theoretical background needed to make correct judgments concerning potential aggregate supply changes. As energy prices increase, the farm manager encounters higher production costs. The manager must then adjust his cropping mix so that profits are maximized. If it is assumed that the farm produces corn and soybeans, Figure la demon- strates how corn and soybean acreages change as energy prices increase. The curve C represents the various combinations of corn and soybean output that can be grown at the same cost on a given farm. The slope of line PR indicates the level of the soybeanzcorn price ratio; the steeper the slope, the higher the ratio. If PR is moved until it is just tangent to curve C, the correct combination of corn and soybeans is found. If energy prices increase, the curve changes to a posi- ltion similar to C . Notice that C l 1 7 is considerably farther Corn Acreage u l u Corn P131 (a) Corn Acreage Soybean Acreage (b) Corn Acreage ql qzc Soybean Acreage Figure 1. Effect of increased energy prices on enterprise combinations. from C on bean axis b corn. Line The higher c ll, and corn Figure assumed that increase in “We of lin anew point and corn out qz ' ql and aurerical ex: I l‘I‘Cre'ASES an: .C . 0‘ APPendix ,: AggIEga tion leVEl ch CCmodi ty . 3'2” .:.egate SO; I I], As the ; Mainis . Th | in . iterlstics a. Tte . Tune how iiSti n“ Point “C “l from C on the corn axis relative to the distance on the soy- bean axis because energy prices have a greater effect on corn. Line PR moves down to PR1 and retains the same slope. The higher costs cause soybean output to increase to q2 from ql, and corn output decreases from 111 to u2. Figure lb illustrates how output changes if it is assumed that an energy price increase is equivalent to an increase in soybean price. Curve C remains stable, but the slope of line PR changes to PR1. The tangent point moves to a new point on C. Soybean output increases to q2 from ql, and corn output decreases to 112 from ul. For a given farm, qz - ql and 112 - ul should be the same in both 3a and 3b. A numerical example of the equivalent effects of energy price increases and soybean price increases is given in Exhibit A2 of Appendix A. Aggregate Supply Responses Aggregate supply change is the summation of the produc- tion level changes on all of the farms producing the given commodity. Two theoretical methods often used to analyze aggregate supply are comparative statics and cobweb analysis [1]. As the name implies, comparative statics is a static analysis. This type of analysis looks at supply-demand char- acteristics at distinct points in time, making no attempt to determine how conditions change during the periods between the distinct points in time. Figure 2 is an example of the use of comparative statics. Price 10 Price Corn Price Soybeans 2 S / P2 P l / K P1 / D //// D qqu qqu Quantity Quantity Figure 2. Industry supply responses caused by energy price Increases. Energy prices increase and the cost of producing corn and soybeans increases, causing a disequilibrium. A new long- run equilibrium is attained when aggregate supply decreases to S1 from S and prices increase to P2 from P1' Notice that the shift in S1 for soybeans is less than the shift in S1 for corn and that the price increase is greater for corn, since corn requires more energy inputs than soybeans. But compara- tive statics (as represented by the graphs) does not show the short-run changes that occur in the process of regaining equilibrium. The cobweb analysis can be very important because it indicates the series of short-run supply and price adjustments that occur before long-run equilibrium is reached. Figure 3 gives an example of cobweb analysis for the effects of increased energy prices on corn and soybean supplies. Tomek and Robinson [2] suggest allowing fo and soybean prices MM and soybean Since quant Prices Chan; 11 [2] suggest that the analysis can be made more realistic by allowing for shifts in supply and demand curves. The corn and soybean supply curves move to S from S because energy 1 prices increase. Initial equilibrium is at P0 and ql. Corn and soybean prices change to P1, causing q2 to be produced. Since quantity q2 is not at the new equilibrium quantity, prices change to P Eventually, the new equilibrium point 2. at the intersection of S1 and D is attained. Using S1 in the analysis tends to shorten the period required to reach the new long-run equilibrium point. It may be appropriate to shift the demand curve also, but the probable long-run effect of energy price increases on demand is difficult to predict. This analysis is also modified by the fact that farmers base production plans on both past price and expected price. By anticipating aggregate production changes and the probable prices resulting from these changes, the farmer adjusts his production to reflect probable prices. This causes a shortening of the cobweb cycle. The cobweb analysis above indicates the series of short- run equilibriums attained before the new long-run equilibrium is reached when energy prices increase. The following numerical example demonstrates how the long-run equilibrium prices for corn and soybeans change when energy prices increase. The average total cost curve increases for both corn and soybeans. If it is assumed that long-run equilibrium exists with corn at $2.25 and soybeans at $4.50 before energy.prices increase, how much do corn and soybean prices have to increase to equal Price Price "U III 12 Price Corn 51 S P3 P230 I l // D q2‘34 q1‘13 Quantity Price Soybeans ‘\\\\\ S -3' P1 _1 P2 P 0 ./ ///// D / I .q3q2q1 Quantity Figure 3. Revised cobWeb with supply curve adjustment. minimum ave prices incr average yie and 38 bush increases 1 for soybean for corn an Egg Corn Stock feedi both the en feed ration Vary within CEpendS On l3 minimwm average total cost? If crude oil and natural gas prices increase to $9.06 and $1.49, respectively, and if average yield is assumed to be 110 bushels per acre for corn and 38 bushels per acre for soybeans, average total cost increases 12 cents per bushel for corn and 4 cents per bushel for soybeans. :The long-run equilibrium prices become $2.37 for corn and $4.54 for soybeans. Effects on Livestock Supplies and Prices Corn and soybeans are imperfect substitutes in live- stock feeding enterprises.' In other words, livestock need both the energy in corn and the protein in soybeans in their feed rations. The ratio of corn to soybeans in a ration can vary within a range, and the ratio chosen within this range depends on the soybean:corn price ratio. The imperfect sub- stitutability has some impact on corn and soybean supply adjustments. A significant decrease in corn supply with a con- current increase in soybean supply may cause livestock feeding to decrease. The livestock demand for soybeans decreases. Large short-run price variations hicorn and soybean prices occur. The change in the long-run equilibrium of cOrn and soybeans caused by energy price increases has an effect on livestock production. Figure 4 indicates possible adjustments in livestock production. Curve C represents the combination of corn and soybeans that can be supplied by the farm sector for the same cost. Curve R represents the combinations of Corn 14 Corn C C “I Sofiheans Figure 4. Potential adjustments in livestock feeding. corn and soybeans that can be fed to livestock to_generate the same revenue. When energy prices increase, curve C de- creases to C1. To regain optimal conditions, curve R de- creases to R1. Both revenue and livestock production decrease. Supplies of livestock products decrease which causes price increases. The long-run response of fed live- stock prices is to increase by an amount which approximates the increase in production costs of the livestock. Livestock enterprises that require a large amount of corn Or a rela- tively large ratio of corn to soybeans in their ration become more expensive. Thus, poultry products could become cheaper relative to pork and beef. But, in general, the price of livestock products increases. [l] [2] 'Ulrf H [1] [2] 15 REFERENCES Scott, Robert H., The Pricing System. San Francisco: Holden Day, Inc., 1973, pp. 166-168. Tomek, William G. and Robinson, Kenneth L., A ricul- tural Product Prices. Ithaca: Cornell UniverSIty Press, 1972, pp. 176-181. Increa tilizer cost in turn caus decrease, ,2 farmer to re Would a SWit drying, bOth FiZe PrOfits fishering th T0 att Amine the EnterpriSes linear prOgr Ciently SEIe CHAPTER III DEVELOPMENT OF A DECISION MODEL Purpose of Model Development Increasing petroleum prices has caused fuel and fer- tilizer costs to increase. These increased input expenses in turn cause the potential profitability of farm firms to decrease. Are there adjustments that can be made by the farmer to restore potential profitability to previous levels? Would a switch to short season corn hybrids and longer field drying, both of which require less energy for drying, maxi- mize profits? As implied in the objectives in Chapter I, answering these questions was the primary goal of this study. To attain this goal, a method should be derived to de- termine the proper adjustments of various corn and soybean enterprises accurately and realistically. For this purpose, linear programming (LP) was used, since this technique effi- ciently selects the strategy that will maximize profits given various price and resource constraints for an individual farm. To develop the model, a hypothetical farm is constructed to represent a "typical" agricultural unit. This procedure is defined as economic engineering. The characteristics of this farmiare quantified and placed in the LP model. Internal characteristics, such as farm size, soil type, fertility levels, cropping enterprises, and machinery types and sizes 16 are selectec istics, sucI affect the f Characteris inate real the solutior corn and soy mize profits Result Per adjustme mize profits that every 1 in the Same Cation 0f hc Aquarium. 17 are selected. Decisions concerning which external character- istics, such as climate, labor availability, and prices, affect the farm are also made. Careful selection of these characteristics of the typical farm allow the model to approx- imate real world conditions more accurately. In this study the solution of the LP model gave the optimal combination of corn and soybean hybrids that the farmer should grow to maxi- mize profits. Results from analysis of the LP model indicate the pro- per adjustments in crOpping mix a farmer should make to maxi— mize profits when energy prices increase. If it is assumed that every farmer with a similar operation makes adjustments in the same manner, it is possible to get a reasonable indi- cation of how aggregate supplies of corn and soybeans change. A qualitative judgment concerning how increased energy prices affect aggregate supplies can then be made. The LP model generated the quantitative data necessary to solve the objec- tives of this study. Assumptions and Description of Typical Farm When reviewing the results of the various analyses of this report, it is essential to know the assumptions on which the analyses are built. The purpose of this section is to discuss the various aSsumptions made in designing the ”typical" farm. The farm assumed has 600 tillable acres composed of a clay loam type soil, is located in Southeastern Michigan, and grows corn corn and SE soil is 11? The ITI (I) one 100 40-50 hp tn and4 row c one with 4- bMIons, (4 I6) one 8 rl meats, and fueled. This in ‘7 Specif Stalks are to plOw Wit Within the followed wj 18 grows corn and soybeans. With good drainage, the potential corn and soybean yield (based on a 10 year average) on this soil is 115 and 38 dry bushels, respectively. The machinery component consists of the following items: (1) one 100-120 hp tractor, one 65-80 hp tractor, and one 40-50 hp tractor, (2) one combine with 12 foot grain platform and 4 row corn head (30 inch rows), (3) two moldboard plows, one with 4-16 inch bottoms and the other with 6-16 inch bottoms, (4) one 14 foot disk harrow, (5) one 16 foot harrow, (6) one 8 row planter with herbicide and fertilizer attach- ments, and (7) three grain wagons. All power units are diesel fueled. This machinery component performs the field operations in a specific sequence. After the crop is harvested, the stalks are cut up with a disk harrow. The land is then ready to plow with the mOldboards, either in the fall or spring. Within the planting period, the land is harrowed and then followed with the planter. All fertilizers, except anhydrous ammonia, are applied during the planting operation. Herbi- cides can be applied during the planting operation or while harrowing. Ammonia can be applied anytime in the spring before, during, or after the planting operation. Mechanical cultivation may be necessary during the growing season. The machinery components can be used in several ways to complete the cropping sequence. Thus, a specific tillage and harvesting method must be selected. Harvesting requires two men, one combine, and one tractor along with grain wagons. One man 0; from fiel< man is in‘ disking s quire all two tract Narrowing operation The pOI‘EIOn ( hours in family II assumed . one hire 19 One man Operates the harvester while the other man hauls grain from field to dryer and tends to the drying operation. One man is involved in the fall plowing operation which includes disking stalks and actual plowing. If harvesting does not re- quire all available time in a period, then, as in the spring, two tractors and two men are used in the plowing operation. Harrowing requires one man and tractor as does the planting operation and ammonia application. The farm owner and his family supply a significant portion of required labor. The owner is assumed to work 10 hours in the field on days with good weather conditions. Other family labor is supplied by children still in school and is assumed to amount to an average of 4 hours per good day. One hired man supplies an additional 10 hours of field time per good day. During spring and fall periods work is per- formed on Sundays if the weather is acceptable. To determine drying capacity and fuel requirements for drying, a specific dryer must be selected. In this problem a 100 bushel capacity continuous flow dryer capable of deli- vering 13,000 cfm of air heated to a temperature of 185°F was chosen. The fan is powered by a 4 horsepower electric motor. As stated previously, the farm produces corn and soybeans. The owner can make adjustments to internal and external fac- tors affecting his production process by planting and harvest- ing various combinations of corn and soybean hybrids (as well as different acreages of corn relative to soybeans) during various planting and harvesting periods. Yield and moisture content va: planting ar season corn as a perce: in parenthe for soybean and moistur limited. A was invest 1 It was sung: would be veI tive lUdgmer hybrids are Potential yi GXCess fiel ha'te discoun ’41 market 1 4} “Mounted E Data 1 Abdel were c hater ‘ e heed E Altho1 IE 5 been pre Are and wO] 20 content vary during the harvest periods. Table 1 lists the planting and harvesting periods for short, medium, and long season corn hybrids along with the corresponding yield (given as a percent of potential yield) and moisture content (shown in parentheses as a percent). Table 2 gives yield information for soybeans. Data on potential soybean yield, field losses, and moisture content at various stages of maturity are very limited. A table containing limited data on this subject [1] was investigated in conjunction with a soybean specialist [3]. It was suggested that prediction of yield and moisture content would be very difficult to specify precisely. Thus, subjec- tive judgment was used. Early planted and early harvested hybrids are assumed to yield near maximum potential. Below potential yields are due to either high moisture content or excess field loss. Therefore, early harvested varieties may have discounted yields because moisture content is above opti- mal market levels. Later harvested varieties have yields discounted because of excessive field loss. Sources of Information Data used in the development and calculation of the medal were derived from numerous sources. These sources are referenced at appropriate points throughout the paper. Structure of the LP Model Although a brief description of what an LP model does has been presented, a more thorough description of its struc- ture and workings is necessary. An LP model is a series of Table 1. E Hybrid and Harvesting Sept. 15-30 85 day 100 day 115 day Oct. 1-14 85 day 100 day 115 day Oct. 15-30 85 day 100 day OCt- 31-Nov. 33 day 100 day 115 day 3°," 15-Dec. 85 day 930 day ‘15 day \ Source: B la Ag: Sta 21 Table 1. Expected Yield and Moisture Content of Corn Hybrid and Planting Dates Harvesting Dates April May May May May 30- 20-30 1-9 10-19 20-29 June 10 Sept. 15-30 85 day 83(26) 83(28) 100 day 92(30) 115 day Oct. 1-14 85 day 82(21) 82(23) 80(26) 78(30) 100 day 90(26) 83(28) 115 day 100(30) Oct. 15-30 85 day 78(18) 78(20) 78(23) 75(26) 72(30) 100 day 87(22) 87(24) 83(27) 78(30) 115 day 98(26) 97(28) 90(32) Oct. 31-Nov. 14 85 day 73(18) 73(18) 75(20) 72(22) 68(24) 100 day 82(20) 82(22) 79(23) 75(26) 68(25) 115 day 93(22) 93(24) 85(26) 75(30) 68(32) Nov. 15-Dec. 1 85 day 67(19) 68(19) 71(19) 68(21) 65(22) 100 day 75(20) 76(22) 73(22) 70(23) 63(26) 115 day 88(20) 88(23) 79(23) 70(25) 62(28) Source: Black, J. Roy, "Farm Planning Guide: Corn vs. Beans," Agricultural Economics Staff Paper 1974-12, Michigan State University. Table 2. Hybrid and Harvesting Sept. 15-3 117 day 123 day 128 day Oct. 1-14 117 day 123 day 128 day Oct. 15-30 117 day 123 day \ linear eque tion aCtivj level 0f te be PreSent‘ lation- Ne f0! Attain; Present Wh; if. the var: which maxir The r MaXir 22 Table 2. Expected Soybean Yield Hybrid and ’ Planting Dates ‘ Harvesting Dates May 10-19 May 20-29 May 31-June 10 Sept. 15-30 117 day 37.0 38.0 123 day 38.0 128 day Oct. 1-14 117 day 34.61 123 day 33.25 33.25 31.92 123 day 35.95 35.95 Oct. 15-30 117 day 23.20 123 day 24.30 128 day 25.80 linear equations which show the relationship between produc- tion activities and resources constraints, subject to a given level of technology. To form a LP model, three elements must be present. First, a goal is needed, such as profit maximi- zation. Next, there must be alternate methods or processes for attaining this goal. Finally, there must be constraints present which limit the amount of resources available for use in the various processes. The model selects the one process which maximizes profit subject to the resource constraints. The model can be described mathematically also. n Maximize Z = z r x. n Subject to: z a.. < bi' for i = 1,2,. . .,m, and X lv 0, for all j. The fir functio example short s Septemb produci activit Constra There a 0f the bit is effiCie unit of f0r 1am l'ld a1: I'unire all act F: 30691. 9R6 92 fie . SCI-l] 1“ Exa. 23 The first equation is the profit maximization or objective function. The model contains n activities, or xj's. For example, activity x2 might be the production of one unit of short season corn hybrid planted April 20-30 and harvested September 15-30. The rj is the revenue (or cost) generated by producing one unit of xj. Summation of the products of the activities and their respective revenue equals profit. The constraining resources are presented in the next equation. There are m resource constraints present. The total amount of the ith resource available for use is bi‘ This amount, bi' is allocated to the various xj activities. The aij co- efficient is the amount of hi resource used to produce one unit of Xj. For instance, if i = l is the reSource equation for land, b = 600 means that 600 acres of land is available 1 and a e 1 means that each unit of corn produced (x2 above) 12 requires one acre of land. The last equation guarantees that all activities are at zero or positive levels. Figure 5 is a simplified visual description of the LP model. The columns represent activities and the rows are resource constraints. There are 131 activities (n = 131) and 92 constraints (m = 92) in the tableau. A more complete description of the components of the LP tableau is presented in Exhibit A1 of Appendix A. In the discussion of the assumptions used to derive the model, it was emphasized that tillage and harvesting activities occur in a specific sequence. The simplified flow chart in Figure 6 clarifies the production procedure. LIi a In 0.0.20-b 0.0.0.0..— ..)l-s Ivan!- IS-SSDQI Icu’t-L uni. IOO..uhIL ran—Inna... o-Io~n r—-.nc— 0:-cc...~ I . NNKILINIIII- h _ . h . I .1 III — ~ _ ~ NI NT .\ . N . dials-0‘69 ‘3...- ‘ . - ifliwfl Iluuiu ll..I.-l Henri-4H4 III 5.3... I-—&L( I...)5I: ‘nu'OPbl EUNISChh II-EBLS. Inn—LC! EIOKDEM 00-bububh ‘05-: .—I€vtl( ‘00:)Cr {5.3 I‘uu‘lu‘ ‘II naIL «unoffiu Cull. vc-Iro no.9.- Ina.tx.~0 5..-:- utda istuu nuIno -¢-~n he - I'-nA-IEP lbs- .I .L:.-‘ 24 I33 ' i guano—e . . . nun-ago «5...: 7 \ .\ 2:95.38 :0»...- II \\\.\.\\\I :1: \MM W\\\.\\\ «30:38 28: § Q§ canes ecu-3.2.6 30...... I 2.3.2.: \ In. H . . I I. . \\\«-.0. .\ I \ Peace:— .335 III II. I, Auummuvxx II I e: .\\\..\.. on: use:— \\ I «0:: \\..., 395.25 «55.5 \ . \. if... . I I on“... a-.. \ \ ‘1 I h \\ \ k SIN! . \\ \. . _ .5" «3.6.5:.— . p . n I n l— ll. l I! II. .I I . . 23.1. V V \\ .3: goof—a.. a.. . \ . ~c.§.o~ E3302.— S. 25: MN \ \\ \\ \ . .. \N\\\mfi\ ..\. 25.3-: \ . .e I. A; N t . _ \ AWMNNAWNN. § . has... 3: RN. \ .\N« {I be... \\.\A .- A a....II . \\\q\\ x \\ \\ \ \ .1\ w . \\ \ ., .. . \ \ \ X \ \ x h .x \A \.\n\ . x \ x... C . .3... :8. I i w I\\\\\\\ \\\\\\. \ \\\\x . t . 24 . 5536.2.— 950 i n . . .3... 1.: II: \ _ ~ A \.\I " 03932.00 ‘1— I I II A 3.333.— 382.99— 3233 31.3 :39: Iago-Co: 3:?- uOuooonh c3331. «3:3 39.33 .333». . 3.5:... .33: :8 32:: 25. .29.: :25 £8 2:3: 3. z... :75 58 . «In... .24: A 3.3: :78... 37: 2.-.. 5.5.; 3.: :12 .3. :5 3.2 a-» .8 SS: suoandh 3 .n Una-nah 25 .uumno 30am mcowumuomo paofim mcmonhom HHom Chou Haom Shoo >Dc cuco mammnmom Osman ucmam wcflpem pang mflcosem m :Hou Bonus: maee< Im umo>umm same seesaw tam; 30am puma 30am Ceca coumo>umm \ mcmwn%om umo>umm .m Tasman By use of productic circular. for fall is availa in the fa been plow Planting Cannot ex COrn must rowing or CritiCal seqUently sol’b‘edns haIVested 26 By use of transfer rows and columns in the linear program, the production sequence can be specified. As shown, the flow is circular. Land harvested in a fall period becomes available for fall plowing in that or subsequent periods, if field time is available after harvesting requirements. Land not plowed in the fall is plowed during a spring period. Land which has been plowed is available for harrowing in a spring period., Planting must occur in that same period (planting in a period cannot exceed harrowing in that period). Acreage planted to corn must have ammonia applied either before or after har- rowing or after planting. Timing for this operation is not critical as long as all land that receives ammonia is sub- sequently planted with corn. During the fall period corn and soybeans are harvested. This acreage becomes part of the harvested acreage stock, thus completing the circle. Soybeans harvested are sold. Corn harvested is dried and then sold. Data Calculations When data were derived fOr use in the LP model, calcu- lations were made using the assumptions discussed earlier along with other facts. This section gives examples of each type of data calculation. (1) dry corn yield - Yield is derived from information given in Table 1._ The dry yield is the percentage figure given in the table multiplied by the maximum potential yield, 115 bushels/acre. As an example, short season corn planted in the first spring period and harvested in the first fall period yields 1 for each (2) 2. Refe this tab (3) data for See Tabl good day number 0 in Previ hired 1a 24 times 2Pfiber o for APri ll 27 yields 115 times .83, or 95.45 bushels per acre. The yield for each corn activity is given in Table A1 of Appendix A. (2) soybean yield — Yield is shown explicitly in Table 2. Refer to the discussion of assumptions used in deriving this table. (3) time availability for field operations - Weather data for spring and fall periods were obtained from Black [1]. See Table A3 of Appendix A. By multiplying the percent of good days times the number of calendar days in a period, the number of days available for work is determined. As stated in previous assumptions, 24 hours of operator, family, and hired labor are available each day. Thus, multiplication of 24 times the number of good days in a period gives the total number of hours in a period available for field work. Example: for April 20-30, 11 days x .45 good days = 4.95 working days 4.95 working days x 24 hours labor/working day = 119 hours. Results for each period are given in Table A2 of Appendix A. (4) family labor availability for field operations - Fourteen hours of operator (10) and family (4) labor are available on a good day. It is assumed that family labor will be depleted before other labor is hired. Therefore, it is necessary to determine the amount of family labor available each period. Example: for April 20-30, 4.95 working days x 14 hours/day = 69 hours. Results for each period are given in Table A2 of Appendix A. 28 (5) field efficiency of tillage and harvesting opera- _t__i_gn_s_. - Field efficiency percentages were derived from data presented by White [5]. It is necessary to determine the time required to perform one acre of field operations. For fall plowing one man operates a disk and a plow. The 14 foot disk moves at 5 mph at an efficiency of 85 percent. If the formula given by White is used, efficiency equals (14 ft. x 12 in./ft. x 5 mph x .85)/100 = 7.14 acres per hour. The tractor and 6-16 inch moldboard move at 5 mph and an efficiency of 85 Percent, or 4.08 acres per hour. Transforming these two rates into hours per acre and totaling gives a time requirement of 383 hours per acre (1/7.l4 + 1/4.08) for fall plowing. Since the largest tractor is used to pull the planter during spring Periods, the spring plowing rate is slower due to use of a smaller plow. In the spring a 4-16 inch bottom plow moves at 5 mph and 85 percent efficiency to give a rate of 2.74 acres per hour. This gives a total time requirement of .507 hours per acre for Spring plowing. The 40-50 hp tractor pulls a 16 ft. harrow at 5 mph and an efficiency of 80 percent to give a rate of 7.68 acres/hour, or .1302 hours per acre. The 100-120 hp tractor pulls the 8 row Planter at 4 mph and an efficiency of 60 percent to give a rate of” 5.76 acres/hour, or .1736 hours per acre. It is aSsumed that the corn and soybeans can be planted at equal rates. Ammonia is applied with the 65-80 hp tractor pulling a 4 row applicator at 5 mph and an efficiency of 75 percent to give a rate of 4.5 acres per hour, or .2222 hours per acre. Cc at a spe of 2.16 and ham by two. are com] an effi- After t vesting occur 1 morning that sc hours ] dix A Vary f of 30y Costs Al 0f fertit are C 50: a has 29 Corn is combined by the use of a 4 row head travelling at a speed of 3 mph and an efficiency of 60 percent for a rate of 2.16 acres per hour. Since time is measured in man-hours and harvesting requires two men, this rate must be divided by two. This gives a rate of .93 hours per acre. Soybeans are combined with a 12 foot grain platform moving at 3 mph and an efficiency of 60 percent to give a rate of 2.59 acres/hour. After transforming and considering the two men needed for har- vesting, the rate becomes .77 hours per acre. A problem may occur in soybean harvesting because of dew or fog in early morning hours which prevents harvesting. Thus, it is assumed that soybeans and corn are harvested at the same rate of .93 hours per acre. (6) crop_variab1e cost budget - See Table A4 of Appen- dix A for specific budget. Variable costs of corn production vary from.$28.92 to $35.04, depending on hauling costs. Costs of soybean production vary from $23.14 to $24.21. Specific costs for each corn and soybean activity are given in Table A1 of Appendix A. These values do not include the costs of fertilizers, fuel, drying, and seed. These particular costs are calculated by the LP model. See Table A5 in Appendix A for an example of total variable cost for a particular corn and soybean activity. Table A9 in Appendix A lists the items in the machinery component and the annual fixed costs of owning and operating the farm. (7) diesel use - See Table A5 of Appendix A for a specific listing of uses. Each corn activity uses 7.07 gallons of diesel (8) fic amoun marketabl mine dryi: prepared 1 activity (. corn at 1! bushels 0: equals 56 1000 by 8'. 26 Percent a value of m.c, COnta water to t is 14.56 t in one bus of Water, of Corn is (9) specified give“ perj be found; Per he“, ing equati E: 30 of diesel and each soybean activity uses 5.68 gallons. (8) moistureyremoval - For each corn activity a speci- fic amount of moisture must be removed to get the corn into a marketable condition. This information is then used to deter- mine drying capacity and propane use. Through use of a table prepared by Uhrig and Strom [4], the wet corn yield of each activity can be determined. For example, 95.45 bushels of corn at 15.5 percent moisture content is equivalent to 109.62 bushels of corn at 26 percent moisture content (a bushel equals 56 pounds). This is derived by dividing 95.45 times 1000 by 870.74 (amount of dry corn in 1000 bushels of corn at 26 percent m.c., as found in the table). This calculation gives a value of 109.62 bushels. One bushel of corn at 26 percent m.c. contains 14.56 pounds of water. The total amount of water to be removed from one unit of this activity (one acre) is 14.56 times 109.62 minus 95.45 times 8.68 (pounds of water in one bushel of corn at 15.5 percent m.c.), or 767.64 pounds of water. The amount of water removed by drying each acre of corn is given in Table A1 of Appendix A. (9) drying capacity -.For the continuous flow dryer Specified a certain amount of moisture can be removed in a given period. 'First, the water removal capacity per hour must be found. The dryer can produce a specific amount of BTU's per hour, depending on environmental conditions. The follow- ing equation specifies the energy rate: E = V01 x SpV x (Ca + CVH) AT x 60 1/Eff E=e Vol=a SpV=s Ca=c Cv=c H=. AT='1 Eff:6 Thmugh USE] SOUtheasteI ing anSWer 3:1 )5 I “Ount of ‘R ing the amcl from the “El example abcl H20/11)a = can be Calq Cap = h'hEre: Cap = V01 - 31 where: E = energy rate in Btu/hour V01 = air flow in ft3/minute SpV = specific volume of air in 1ba/ft3 C = a constant equal to .242 Btu/lba°F C” = a constant equal to .45 Btu/lbv°F H = absolute humidity in lbv/lba AT = T °F hot - Tambient 1n Eff efficiency of dryer Through use of average temperature and humidity figures for Southeastern Michigan (see Table A6 in Appendix A), the follow- ing answer is found for the September 15-30 period: E = 13000 x .0753 x (.242 + .45 g .0074) x (185-61) x'60 x (1/.5) = 3,573,432 Btu/hour. From a psychometric chart it is possible to determine the amount of water removed by a pound of heated air by subtract- ing the amount of water in a pound of air entering the dryer from the water content of the air leaving the dryer. For the example above, this is .0299 lbs. of H20/1ba - .0074 lbs. of Hzo/lba = .0225. With this information the drying capacity can be calculated as follows: .- Cap V01 x SpV x 60 x WR where: Cap drying capacity in lbs. of water removed per hour V01 = as above SpV WR From previ Cap Now, mined. Th. hour times period. P; harvesting as many ho: because dr} | ditions are following CI Cdpag r‘otal Capac “PPendix A (10) quled wi th F hua. ‘ Priate leVe i Iding the f . Prom; 32 as above 0: '0 < ll WR difference in water holding capacity of air enter- ing and leaving the dryer From previous calculations, Cap = 13000 x .0753 x 60 x .0225 1321.5 lbs. of water removed per hour. Now, drying capacity for the whole period must be deter- mined. This is done by multiplying the drying capacity per hour times the number of hours available for drying during the period. For the September 15—30 period 10.08 days of favorable harvesting conditions are available. It is assumed that twice as many hours are available for drying operations as harvesting because drying can occur at night and on days when weather con- ditions are good but field conditions are not. Thus, the following calculation is made: Capacity = 10.08 days x 2 x 10 hrs./day x 1321.5 lbs. HZO/hr = 279364.4 pounds of water. Total capacities for each fall period are given in Table A2 of Appendix A. (10) propane use - It is assumed that the dryer is fueled with propane. Calculations are made to determine the number of gallons of propane used to dry corn to the appro- priate level for each acre of corn activity. This is done by using the following formula: PropU = [(MC/DCap) x E] x l/Cp x l/Dn x Cg where : Pro; Using this PrOpl Propane u5€ APPendix A. (11) energy 501.1]: tricity USe E1U = wheIe: Em .. HP II MC II 33 where: PropU propane use in gallons MC = water to be removed when drying one acre of corn in lbs. H O 2 DCap = drying capacity in lbs. of water per hour E = energy use in Btu per hour constant of 19944 Btu/pound of propane 0 II D = density of propane in pounds per cubic foot C = constant of 7.48 gallons per ft3 of propane. Using this formula for the September period, PropU = (767.64/1321.5) x 3573432 x 1/19944 x 1/31.75 x 7.48 = 24.56 gallons of propane. ~Propane use for each corn activity is given in Table A1 of Appendix A. (11) electricity use - Although propane is the primary energy source for drying, electricity is used to run the fan and augers. The following formula is used to determine elec- tricity use of the dryer: E1U = Ce x HP x l/Eff x MC x l/DCap x 1.10 where: M H C'. II electricity use in kilowatt hours C = constant of .746 kilowatts per horsepower HP = constant of 4hp for the motor specified MC = as above DCap as above. For the Se to account I 310 ’ Data for e in Table A (12) com depen gen should the fertil duction, the Optima be determiy YiEId of 9. nitrogen a 120 Pounds' are ginn ‘1 Phos} referrins 34 For the September period,and adjusting by a 10 percent factor to account for electricity use by augers, E1U = .746 x 4 X l/.45 x 767.64 x 1/1321.5 x 1.10 4.23 kilowatt hours Data f0r electricity use for each corn activity may be found in Table A1 of Appendix A. (12) nitrogen use - The amount of nitrogen applied to corn depends on the economic returns of application. Nitro- gen should be applied up to the point where marginal cost of the fertilizer equals marginal revenue of the increased pro- duction. Through the use of a table prepared by Black [1], the optimal amount of fertilizer for the given yield level can be determined. For example, a corn activity with an expected yield of 95 bushels and with corn at $2.50 per bushel and nitrogen at 15¢ per pound, the optimal application rate is 120 pounds per acre. Optimal rates for each corn activity are given in Table A1 of Appendix A. Phosphorous and potash application rates are found by referring to Extension Bulletin E-550 [2]. For expected corn yields above 100 bushels per acre phosphorous is applied at a 60 pound per acre rate and potash at a 50 pound per acre rate. "For yields in the 85-100 bushel range a 50 pound rate for phosphorous and a 40 pound rate for potash should be applied. For yields less than 85 bushels 30 pounds of phos- phorous and 25 pounds of potash are applied. A standard rate of 50 pounds of phosphorous and 30 pounds of potash is appliedi to each acre for soybeans. (13 model two is the tr tions whic time cons each opera is 97 how has been 0 for harrow figure was 24 hours ( hours fami per day, a1 which gives :. 35 (13) time constraints on field operations - In the LP model two methods are used to limit field operations. One is the transfer rows and columns for the various field opera— tions which insure the proper sequencing of operations, given time constraints. But another time constraint must be put on each operation. For instance, time available for field work is 97 hours for the second spring period. This calculation has been discussed previously. But 97 hours are not available for harrowing because only one harrow is used. The 97 hour figure was derived by multiplying the number of good days by 24 hours (10 hours Operator labor, 10 hours hired labor, 4 hours family labor). Harrowing is performed only 10 hours per day, and, therefore, 97 is multiplied by a 10/24 factor which gives 41 hours. To put the constraint into an acreage figure, multiply 41 x 7.68, or 314 acres. Constraints for each field operation are given in Table A2 of Appendix A. A few adjustments were made on some constraints. For fall plowing in the last fall period and spring plowing in the first 'spring period additional plowing time was added. It is assumed that 20 hours of field time is available for plowing during the post-December 1 period and the pre-April 20 period. This increases plowing capacity. An adjustmentwas also made for planting during the April 20-30 period. The time avail- able figure derived from weather data for this period is Optimistic for planting operations. Therefore, it is appro- priate to reduce this time constraint for the April 20-30 period by 50 percent for the planting operation. (14) are chosen inputs and dix A list: (15) a rate of beans are I (16) decreases, hour increg than 100 b. by five pez activities 36 (14) prices - For the initial model, specific prices are chosen which should approximate prices for the various inputs and outputs in the 1975 cr0p year. Table A7 of Appen- dix A lists the assumed prices. (15) seeding rates - Corn is assumed to be planted at a rate of .25 bushels per acre for each corn activity. Soy- beans are planted at .83 bushels per acre. (16) harvesting rates changes - As the yield of corn decreases, the amount of acreage that can be harvested per hour increases. White [6] suggests that for yields of less than 100 bushels time requirements for harvesting decrease by five percent. This increase is added to the appropriate «activities in the model. [l] [41 [6) [1] [2] [3] [4] [5] [6] 3 7 REFERENCES Black, J. Roy,"Farm Planning Guide: Corn vs. Beans,“ Agricultural Economics Staff Paper 1974-12, Michigan State University, 1974. Christenson, D. R., et al., Fertilizer Recommendations for Michigan Vegetables and Field Crops, Michigan State University Extension Bulletin E-550, Farm Science Series, November, 1972. . Hildebrand, Stuart, Associate Professor, Soils and Crop Science, Michigan State University. Interviewed in March, 1975. Uhrig, J. and Strom, Jay L., Economics of Drying Corn, Purdue University Cooperative Extension Service, Extension Bulletin EC-390, February, 1970. White, Robert, Fuel Requirements for Selected Farming Operations, Michigan State University Extension Bulle- tin E-780, February, 1974. White, Robert, Selecting a Corn Harvesting System, AEIS No. 306, Agricultural Engineering Department, Michigan State University, August, 1974. {'2' "5"1‘.“ V . and pla C051 5011 The corn and Pr0d1 CHAPTER IV MODEL RESULTS UNDER PRESENT CONDITIONS Explanation of Model Results In Chapter III an extensive description of the LP model and the farm it represents was given. This description ex- plains the basic Operation Of the farm, inputs and their costs, and expected output yields. In this chapter the re- sults of operating the farm in an Optimal manner are given. The more important results include operating income, optimal corn and soybean mix, total energy input usage, total corn and soybean output, and the factors that constrain or limit production. Operating income is the amount of revenue remaining from sale of corn and soybeans after payment of all cash ex- penses (variable costs), including all energy inputs, seed, repairs, and hired labor. Operating income is the amount of funds available to cover machinery overhead (depreciation, interest on machinery investment, insurance), family and Operator labor, interest on equity investment in land and buildings, and management costs. A look at changes in Opera- ing income level will reveal a good indication of net pro- fitability Of the farm.p The model lists which corn and soybean activities are present in the optimal solution. These activities comprise 38 Fro med eacl det: othe only linu the Beca know pure can reSu. sent, is al that If on for l Sitio; “00 i. 39 the crop mix which generates the greatest Operating income. From the list of optimal activities, the amount of short, medium, and long season corn and soybean hybrids planted in each spring period and harvested in each fall period is determined. gSOme cropping activities are more profitable than others. Thus, the optimal solution would be to engage in . only the most profitable enterprise. But resource constraints limit the production of the most profitable activity, and the firm may then engage in less profitable activities. Because constraints do limit revenue, it is important to know which resources constrain the model and how much the purchase of additional amounts of the constraining resource can increase income. This information is listed in the model results. Not only is the amount of each resource used pre- sented, but the marginal value product (MVP) of the resource is also given. The MVP is the amount of additional revenue that can be generated by using one more unit of the resource. If one unit of the constraining resource can be purchased for less than the MVP, operating income would increase. Thus, MVP is an important factor in determining if resource acqui- sitions should be made by the firm. '- Model Results Under Present Conditions The initial conditions present in the LP model were discussed in Chapter III. The prices Of the various produc- tion inputs and outputs are given in Table A8 Of Appendix A. These 1975 and a of A; from of sc long 236 a 10-19 seaso 40 These prices and conditions approximate those present in the 1975 crop year. The results of the model are discussed below and are also given in tabular form in Tables B4, B5, and B6 of Appendix B. The farm has an Operating income of $83,824 generated from production of 53,108 bushels of corn and 4,081 bushels of soybeans. During the April 20-30 period (81) 144 acres of long season corn are p1anted,followed in 82 (May 1-9) with 236 acres of long season corn being planted. In S3 (May 10-19) 17 acres of short season corn and 95 acres of long season corn are planted. During S4 (May 20-30) 107 acres of short season soybeans are planted. No planting occurs in SS (May 31-June 11). Anhydrous ammonia is applied in the following manner: 31 acres in S3, 263 acres in S4, and 199 acres in SS. During Fl (September 15-30) 107 acres of soybeans are harvested, and in F2 (October 1-14) 144 acres of long season corn and 17 acres of short season corn are combined. In F3 (October 15-39) 148 acres of long season corn are harvested; followed by 145 acres and 38 acres of long season corn in F4 (October 31-November 14) and F5 (November lS-December 1), respectively. Plowing occurs in the following sequence: 107 acres in F1, 162 acres in F2, 71 acres'in F3, 53 acres in F4, 157 acres in F5, and 50 acres in $3. The farm uses 234 hours Of hired labor in the fall periods. The following amounts Of energy inputs are used: 4,093 gallons of diesel, 16,740 gallons of pr0pane, 2,622 kilowatt-hours of electricity, 65,290 pounds (actual nitrogen) of a and stra $113 capa The . acit; high acit] coulc make bEing aCtiv 41 of anhydrous ammonia, 1,074 pounds (actual nitrogen) of ammonium nitrate, 33,800 pounds Of phosPhorous (9205), and 26,726 pounds of potash (K20). Operating income is limited by several resource con- straints. These constraints and their MVPs include: land $113, planting capacity in 81 $35 and $2 $16, harvesting capacity in F3 $11 and F4 $7, and plowing capacity in F5 $1. The MVP values indicate that land resource and planting cap- acity are the two factors that most constrain income. More high profit long season corn could be grown if planting cap- acity were greater in $1 and-S2. If another acre Of land could be rented for less than $113, income would increase. From the results of the analysis it is possible to make several observations. COrn is the most profitable crop, being grown on 82 percent of available land. Most of the corn activitie3(476 of 493 acres) include long season corn hybrids at relatively high moisture contents (23-32 percent) and high 'yields (97-115 bushels). All of the selected corn activities are more profitable than the selected soybean activity. This is apparent because all Of the corn activities are either con- strained by planting or harvesting capacity while the soybean activity is only constrained by the land resource. Effectpof Requiring Low Moisture Corn Activities The results of the initial model suggest that high Yielding, high moisture corn activities, despite their high nitrogen and propane use, are more profitable than soybean and I implz moisi SEdSC cent actix reSpe 42 and lower yielding low moisture corn hybrids. It has been implied that use of short season corn hybrids harvested at low moisture levels could reduce energy use while still maintain- ing income. Two analyses are made, one requiring all long season corn activities to have a moisture content of 25 per- cent or less when harvested and the other requiring all corn activities to have moisture levels Of 25 percent or less. The results of these analyses are given in Analyses 2 and 3, respectively, in Tables B4, BS, and B6 of Appendix B. The most significant effect to investigate is the change in operating income. To eliminate a bias that is created by having excess drying capacity if allowable moisture contents are reduced, variable costs Of each corn activity are re- calculated to include a l.5¢ per point charge for drying. Propane and electricity use is removed from the model. Analysis 46 in Table B4 represents the initial conditions (same as Analysis 1) with an operating income of $79,671. Analyses 2 and 3 have operating incomes of $76,397 and $76,200, respectively. The requirement that moisture contents be 25 percent or less decreases Operating income by $3,274 and $3,451. As moisture content is reduced, the percent- age Of land in corn decreases from 73 to 69 to 63 percent. Thus, anOther effect of reducing drying is to increase soy- bean acreage. A comparison of the operating income of Analysis 1 (on farm drying) with Analysis 46 (off farm drying) gives an indication of the value of a dryer. For the initial CO. 58] ii: the wi] USE 43 conditions the value is $83,824 - $79,671, or $4,153 annually. In this chapter the results of the LP model under pre- sent conditions were presented. These results included a listing of the optimal corn and soybean cropping combinations and the income they generate. In Chapter IV the effects on the farm resulting from changes in input and output prices will be discussed, with the results presented in this chapter used as a standard of comparison. dete a 56 the maxi diti mana Chan. diti< Chang LP mt Price effec analy to in as we Produ CHAPTER V DEVELOPMENT AND RESULTS OF SENSITIVITY ANALYSES Purpose of Sensitivity Analysis As implied previously, the LP model is developed to determine the proper crop mix for the farm assumed. Given a set of input and output prices along with resource levels, the model generates the correct crop combinations that will maximize income. The proper combinations under current con- ditions were given in Chapter IV. But how should a farm manager change his Operations if conditions change? By a change in the inputs to the model to represent the new con- ditions, the model can answer this question. By making changes in the prices Of various inputs and outputs in the LP model, it is possible to determine the effects of these price changes on crop mix. This process of studying the effects of price and resource changes is called sensitivity analysis. Thus, sensitivity analysis is used in this study to indicate the consequences of corn and soybean price changes as well as increases in energy prices on corn and soybean productiOn. Analysis Procedure In this study several types of price variation were considered. First, the sensitivity Of the cornzsoybean crop 44 mi) pri for int sin cro mix at gas and hip 45 mix to changes in the level and ratio of corn and soybean prices was analyzed. Next, the effects Of increased prices for crude Oil and natural gas on the optimal crOp mix were investigated, followed by an analysis of the effects of simultaneous changes in energy, corn, and soybean prices on crOp mix. Finally, a limited analysis of effects on crop mix caused by poor weather conditions in spring and fall periods was made. Pricing_Assumptions One of the major purposes Of this study was to look at the implications of decontrol of crude oil and natural gas prices on corn and soybean production. As crude Oil and natural gas prices increase, the prices of agricultural inputs, such as ammonia, diesel, and prOpane, which are made from crude Oil and natural gas, increase. But to properly analyze the effects on production, values for the relative price movements of the agricultural inputs to a unit price movement of crude oil and natural gas must be determined. For instance, if the price of crude Oil increases by 10 per- cent, by what percentage does the price of diesel increase? Seven inputs in the LP model are assumed to vary with crude oil and natural gas prices. These include diesel, propane, electricity, ammonium nitrate, anhydrous ammonia, phosphorus, and potash. A discussion of their relationships to energy prices follows. Diesel is refined or distilled directly from crude Oil. ir fc fi ei The at is tro 46 Thus, as the cost of crude increases,the price charged by the refiner increases at a rate equal to the crude rate. But the price paid by the consumer must reflect production, transportation, and transactional costs. A study done by Foster Associates [1] states that 56.2 percent of the cost of diesel in Chicago is attributable to production costs. This indicates that a 10 percent increase in crude price would cause a 5.62 percent increase in diesel price, all other factors remaining constant. Of course, as crude oil price increases, transportation costs increase. A precise figure for the rate of increase for transportation costs is dif- ficult to determine since the mode of transportation may be either truck, rail, or pipeline, or a combination of these. Therefore, in this analysis diesel is assumed to increase at 60 percent of the crude oil rate. Propane is a light hydrocarbon in the alkane group. It is present in natural gas and is also a product of the pe- troleum refining process. Because propane can be derived from.both natural gas and crude Oil, estimates of the rela- tionship between propane and these input prices are difficult to determine. Data given by the National LP Gas Association [ 3] suggest that 85 percent of propane (LP gas) is produced from natural gas and 14 percent from crude Oil. Average diesel and LP gas prices in Michigan in July, 1973 were come pared to prices in July, 1975 [5]. In 1973 LP gas cost 86 percent as much as diesel, and in 1975 the percentage was 81. CC A; (e it th 98: nit Cos of Cal nit the: 47 This indicates that, to a large degree, propane prices follow diesel prices. Thus, for this study it is assumed that pro- pane price varies with crude Oil price. The production, trans- portation, and marketing patterns of propane are assumed to be similar to those of diesel, which causes propane to in- crease at 60 percent of the crude Oil rate. Natural gas is the primary input for production Of anhydrous ammonia. Henderson, et a1. [2] list the inputs and costs of the ammonia production process.(See Table B1 of Appendix B.) If the costs are adjusted by a 1.3 factor (excluding natural gas) to account for inflation since 1971, it is determined that natural gas comprises 26.3 percent of the cost of anhydrous ammonia. Thus, it is assumed that anhydrous varies at approximately 25 percent Of the natural gas rate. Natural gas is also a major ingredient Of ammonium nitrate. Table B2 of Appendix B lists the inputs and their costs of the nitrate production process. After adjustments of all costs except natural gas by a 1.3 inflation factor, calculations show that 12 percent of the cost Of ammonium nitrate is derived from natural gas. Therefore, it is assumed that nitrate varies at 12 percent of the natural gas rate. Nitrate and ammonia are also affected by increases in diesel prices. By use Of data from.Henderson, et al., it is calculated that 39 percent of ammonia costs and 36 percent of nitrate costs are for transportation. If it is assumed that 25 percent of transportation costs are for fuel expenses, then phos; rate 48 phosphorous and potash increase at 15 percent of the diesel rate. If both crude oil and natural gas prices are decontrolled, a relative price equilibrium between the two energy sources will occur. An indication Of this relative pricing can be attained by looking at present uncontrolled prices. In the late summer of 1975 intrastate natural gas was selling in the $1.80-$2.00 per Mcf range, and uncontrolled oil from "new“ domestic wells was selling in the $11.00-$12.00 per barrel range. If a linear relationship is assumed, the 1975 control- led gas price of $0.52 per Mcf [4] would suggest a crude oil controlled price of approximately $3.18 perbarrel. But average - domestic crude Oil price is about $7.55 per barrel (40 per- cent uncontrolled at $11.00 and 60 percent controlled at $5.25) [4]. When imported Oil is included, the average prices increase to $9.15 per barrel (64 percent domestic at $7.55 and 36 percent imported at about $12.00 per barrel). This suggests that the current regulated level Of natural gas price is significantly below equilibrium price levels. Thus, when natural gas and crude oil prices are decontrolled simultane- ously, natural gas prices will increase at a substantially faster rate than crude oil prices. In fact, decontrol of crude oil'price on old production will have little effect on the average price paid for oil in the U.S. The domestic market for crude Oil appears to be in equilibrium since supplies are filling demands. Only if demand increases will average price increase, if it is assumed that factors such as embargoes do not occur. Thus,_crude Oil_prices should increa domesi will I study averag to $9. $1.25 crude . natura. relati‘ energy tiVity Varied 49 increase at only small rates to reflect increased demands, if domestic production levels remain constant. With regards to the above discussion, over what range will natural gas and crude oil prices increase? For this study it is assumed that increasing demands could increase average domestic crude Oil price by as much as 20 percent, to $9.06 per barrel.’ Natural gas prices must increase to $1.25 per Mcf to reach equilibrium with the average domestic crude Oil price. If crude price increases to $9.06, then natural gas would increase to $1.49 per Mcf to remain in relative equilibrium. Price Ranges for Each Analysis The sensitivity Of corn and soybean prices,if constant energy prices are assumed, is analyzed first. Price sensi- tivity is measured in two ways. First, corn price is assumed to be constant at $2.25 per bushel, and soybean price is varied from $3.83 to $11.25 per bushel. The range represents a relative price difference (soybean:corn price) from 1.5:1 to 5.0:1. The following analyses are made: (1) corn - $2.25, 33 - $3.33; 1.5:1; (2) corn - $2.25, SB - $4.00; 1.78:1; (3) corn - $2.25, SB - $4.25; 1.89:1; (4) corn - $2.25, SB - $4.50; 2.0:1; (5) corn - $2.25, SB - $4.75; 2.11:1; '(6) corn - $2.25, SB - $5.06; 2.25:1; (7) corn - $2.25, SB - $5.36; 2.38:1; (1 (l (l (1 if the Yses ar broken Crude C decontr that an' Prices I are Cal decennt Prit2e i' ahall's at $2._ 50 (8) corn $2.25, SB - $5.63; 2.50:1; (9) corn $2.25, SB $6.75; 3.0:1; (10) corn $2.25, SB $7.88; 3.5:1; (ll) corn $2.25, SB - $9.00; 4.0:1; (12) corn $2.25, SB - $10.13; 4.5:1; (13) corn - $2.25, SB - $11.25; 5.0:1. To determine if corn mix differs from the above analyses if the absolute price of corn increases, the following anal- yses are made: (1) corn - $2.75, SB - $4.91; 1.78:1; (2) corn - $2.75, SB $5.19; 1.89:1; $2.75, SB (3) corn $5.50; 2.0:1; (4) corn $2.75, SB $5.85, 2.11:1; (5) corn - $2.75, SB - $6.25; 2.25:1. Sensitivity analysis Of energy price increases is broken into three segments: natural gas decontrol only, crude oil decontrol only, and both crude oil and natural gas decontrol. As natural gas price increases, it is assumed that anhydrous ammonia, ammonium nitrate, and electricity prices increase. When crude Oil price increases, all of the energy inputs increase in price. When the price variations are calculated for the analyses below, a 1.05 factor to account'for interest on operating capital is inputted.in the price increases. For natural gas deregulation the following analyses are made with corn and soybean prices held constant at $2.25 and $4.50, respectively: For or $4.50, SamPlea. Of cOr in Cru (l) (2) 1(3) 51 natural gas - $0.70 per Mcf, anyhdrous ammonia - $0.164 per pound, ammonium nitrate - $0.250 per pound, electricity - $0.0307 per kilowatt-hour; natural gas - $0.95, anhydrous ammonia - $0.183, ammonium nitrate - $0.265, electricity $0.0317; natural gas - $1.25, anhydrous ammonia - $0.205, ammonium nitrate - $0.282, electricity $0.0329. For crude oil decontrol with corn and soybeans at $2.25 and $4.50, respectively, the following analyses are made: (1) (2) (3) crude oil - $8.00 per barrel, diesel - $0.394, propane - $0.319, electricity - $0.0301, anhydrous ammonia - $0.151, ammonium nitrate - $0.241 per pound, P 05- $0.241 per pound, K O - $0.101 per 2 2 pound; crude oil - $8.50, diesel - $0.405, propane - $0.330, electricity - 80.0303, anhydrous ammonia - $0.151, ammonium nitrate - $0.242, P O 2 5 - $0.242, K 20' $0.10131 crude oil - $9.06, diesel - $0.428, propane - $0.349, electricity - $0.0304, anhydrous ammonia - $0.152, ammonium nitrate - $0.243, P O - $0.245, 2 5 K20 - $0.102. Sample calculations of the derivatiOn of the above prices are given in Exhibit B1 of Appendix B. To determine how crOp mix varies as the relative prices of corn and soybeans change along with a simultaneous increase' in crude Oil and natural_gas prices, several analyses are made. Energi For ea determ. Varies and $5. Soybear condim- do this follOWj at $4.5 52 Energy prices vary in the following steps: (1) crude Oil - $8.00, natural gas - $0.95, diesel - $0.394, propane - $0.319, electricity - $0.0318, anhydrous ammonia - $0.184, ammonium nitrate - $0.266, p o - $0.241, K 2 5 2 3(2) crude oil - $8.50, natural gas - $1.25, diesel - O - $0.101; $0.405, propane $0.330, electricity - $0.0332, anhydrous ammonia - $0.206, ammonium nitrate - 2 2 (3) crude oil - $9.06, naturalgas - $1.49, diesel - $0.428, prOpane - $0.349, electricity - $0.0343, anhydrous ammonia - $0.225, ammonium nitrate - $0.337, P 0 - $0.245, K 2 5 2 For each step the effects of increasing soybean prices are 0 - $0.102. determined. With corn at $2.25 per bushel soybean price varies at the following levels: $4.00, $4.50, $5.06, $5.36, and $5.63. Each increase in energy prices is analyzed at five soybean price levels to give a total of fifteen analyses. The sensitivity of the Optimal crop mix to poor weather conditions in fall and spring periods is also analyzed. To do this, fall plowing and spring planting are restricted. The following analyses are made with corn at $2.25 and soybeans at $4.50: (1) decrease plowing constraint by 50 percent in each fall period; (2) decrease plowing constraint by 50 percent in F4 and eliminate plowing in F5; A com Table farm < relati $2.25 comple 36 of 16-20 Percen vary, 53 (3) no planting in 81; (4) decrease planting by 50 percent in $1, 82, and S3. A complete listing of all sensitivity analyses is given in Table B3 of Appendix B. Results of Sensitivity Analyses The first two sets of analyses deal with the changes in farm operations that occur when the price of soybeans increases relative to corn price. The first set holds corn price at $2.25 per bushel and the second set at $2.75 per bushel. The complete results of these analyses are in Tables B4,B5, and 36 of Appendix B under Analyses 4-15 for corn at $2.25 and 16-20 for corn at $2.75. Table 3 below lists the changes in percentage of land in corn and Operating income as prices vary. A few observations can be made from Table 3. The per- centage in corn varies from 3-100 percent as soybean price changes. The soybean:corn price ratio must be greater than 1.8:1 before soybean activities enter the optimal solution. There is a relatively gradual decrease in corn acreage as the soybean price increases in the $4.00-$5.60 range. Above this range corn acreage decreases rapidly. Operating income increases as soybean price increases. With corn at $2.75 per bushel corn acreage decreases at a slower rate and initial operating income is larger. Examination Of Tables BS and B6 also shows that long Table SB:Cor1 Price Ratio 1.5:1 1.78:1 1.89:1 2.0:1 2.11:1 2.25:1 2.38:1 2.50:1 3.0:1 3.50:1 4.0:1 4.50:1 54 Table 3. .Acreage and Income Effects of Corn and Soybean Price Changes SB:Corn. Corn = $2.25 Corn = $2.75 Price Ratio SB Percentage Operating SB Percentage Operating Price in Corn Income($) Price in Corn Income($) 1.5:1 3.83 100 82,822 1.78:1' 4.00 100 82,822 4.91' 100 114,200 1.89:1 4.25 91 82,989 5.19 99 114,214 2.0:1 4.50 82 83,824 5.50 91 114,573 2.11:1 4.75 72 85,154 5.85 77 115,955 2.25:1 5.06 63 87,537 6.25 63 118,696 2.38:1 5.36 63 90,060 2.50:1 5.03 60 92,427 3.0:1 6.75 29 109,749 3.50:1 7.88 29 127,639 4.0:1 9.00 3 149,147 4.50:1 10.13 3 171,579 5.0:1 11.25 3 193,813 season corn and short season soybeans are the predominant activities. Only when corn acreage is above 90 percent does a significant amount of short season corn enter the solution. But even then short season hybrids comprise less than 12 per; cent of corn acreage. Long season soybean activities occur as the soybean:corn price ratio moves above 2.5:1. As expected, energy use deClines as soybean acreage increases. Analyses 21-23 in Tables B4, B5, and B6 Of Appendix B give the results of the model generated by an increase in natural gas prices similar to increases that are likely to occur if natural gas price is deregulated. In these analyses corn 1 lists income natura effect energy use de energy hybrid Table 55 corn is priced at $2.25 and soybeans at $4.50. Table 4 lists values of percentage of land in corn and operating income as gas price increases. The results indicate that natural gas price would have to double before a significant effect is made on the amount of corn planted. The increased energy prices do decrease operating income even though energy use declines as the soybean acreage increases. The increased energy prices do not cause a switch to short season corn hybrids. Table 4. Acreage and Income Effects of Natural Gas Price Increases Gas Price ($/Mcf) .52 .70 .95 1.25 Percentage in Corn 82 82 80 73 Operating Income ($) 83,824 82,898 81,660 80,293 The effects of price increases of crude oil are given in Analyses 24-26 in Tables B4, B5, and B6 of Appendix B. Again, corn price is set at $2.25 and soybeans at $4.50. The prices in Table 5 indicate potential increases if crude oil prices are deregulated. The effect on corn acreage is insignificant. The optimal corn and soybean activities re- main constant throughout the oil price range. The increased price causes Operating income to decrease by as much as $1206. .Neither natural gas nor crude Oil price increases alone have a significant effect on the Optimal crop mix. But does the effect become important as gas and oil prices Table . 56 Table 5. Acreage and Income Effects of Crude Oil Price Increases Oil Price ($/barrel) 7.55 8.00 8.50 9.06 Percentage in Corn 82 82 82 82 Operating Income ($) 83,824 83,489 83,225 82,618 __r' increase simultaneously? Analyses 27-41 in Tables B4, B5, and B6 contain the results Of the model, if it is assumed that combined oil and gas price increases and increases occur in the soybean:corn price ratio. Table 6 lists the corn acreage percentage and operating income for these analyses. Corn price is constant at $2.25 per bushel. In general, for a given soybean price level corn acreage de- creases at a slow rate as energy prices increase, particularly when soybeans are $5.00 and less. At higher soybean price levels, soybeans approach the profitability level of corn on a per acre basis, which causes larger decreases in corn acreage as energy prices increase. Operating income increases as soybean price increases for a given energy price level, but income decreases as energy prices increase for each soybean price level. I DO the higher energy prices result in a larger use of short season corn hybrids or other corn activities with low moisture content levels? The answer is no. Only when corn acreage is above 90 percent do short season corn hybrids enter the solution and then only at approximately a level mmuruQUHUEH CUanm 3.8.0 not.» HflO TJOCCCUHJEem N0 maUflMMm QEOUCH Us 004N€>< .0 0134.0 57 mom.mm mm mom.om mm 5mm.om mm th.Nm om mo.m Hma.mm mm 000.0m mm avo.mm mo coo.om mm 0m.m mom.mm ,mo who.vm mo mmv.mm mm hmm.hm mo mo.m mao.mh Np mmh.mh mm mmm.am he c~m.mm Nm om.v mom.mh Hm 5mm.hh mm www.mh mm www.mm ooa oo.v vaoaoocH choc cw AmvmfioocH choc cw .mvwsoocH CHOU ca vamfioosH choc cw mGMUMmeO ommucmoumm mcwumuomo ommusooumm ocwumuomo ommucmoumm mafiumuwmo ommucoouom A.5n\mv 00H mo.amlmm0 .oo.mmnawo mm.aw|mmw .om.mmlawo mm.om|mmu .oo.wmaawo mm.owlmmw .mmrhwudwo cmmnwwm mommouocH ocean new one Hwo msomsouasaflm mo muoommm QEOUGH can cucumbm .m manna 58 equal to 12 percent of total acreage. As in previous analy- ses, energy use declines as soybean acreage increases. One of the most crucial risk factors of farming is the possibility of poor weather conditions. The LP model can be adjusted to determine the optimal cropping decisions, given that weather conditions have limited the time available for field Operations. Analyses 42 and 43 look at the effects Of limiting time available for plowing in the fall. A 50 percent reduction in allowable fall plowing time has little effect on Operating income or corn acreage. The farm has the machinery capacity needed to get the necessary plowing done in the spring. In neither analysis does the crop mix differ from the normal situation. Not being able to fall plow at a normal level (level present under average weather conditions) has little effect on the optimal solution. There is a significant effect when spring planting is limited. Analyses 44 and 45 limit planting capacity by allow- ing no planting in $1 and only 50 percent of capacity in $1, 82, and 83, respectively. Table 7 shows the results. Corn acreage decreases significantly from the normal level, as does Operating income. A relatively large amount of short season corn also enters the solution. Thus, poor weather in the spring increases soybean acreage and short season corn use, but decreases income. 59 Table 7. Acreage and Income Effects of Limited Spring Planting No Planting 50% Planting Normal in 81 S1, 82, 83 Percentage in Corn 75 62 82 Operating Income($) 78,628 77,563 83,824 Short Season Corn 130 75 0 .(Acres) Comparison of Results with Real W0rld Changes Previous discussion suggests that the percentage of land in corn decreases as the soybean:corn price ratio in- creases and energy prices increase. This conclusion is derived from the results of an LP model that finds the optimal behavior for a specific farm. Does this conclusion hold for aggregate corn and soybean production? Table 8 lists his- torical data of soybean: corn price ratios and the percent- age of acreage in corn for Iowa, Illinois, and Michigan. If it is assumed that farmers base planting decisions on price ratios in the past crop year and expected price ratios in the coming crOp year, acreage results in the table indicate that total acreage plantings do respond to changes in price ratios. The acreage percentage does vary in a less volatile manner than predicted by the model, but adjustment does occur. Table 8. Ratios Change Changes in Percentage of Corn Acreage as Price Year Price Iowa Price Illinois Price Michigan Ratio (s) Ratio (s) Ratio (s) 1970 2.14 2.04 2.07 1971 , 2.93 68 2.82 58 2.99 78 1972 3.75 63 3.21 A 55 3.17 77 1973 2.39 59 2.26 52 2.36 71 1974 2.27 62 2.20 54 2.25 74 1975 1.92 63 1.92 56 1.91 75 [1] [2] [3] [4] [5] 61 REFERENCES Foster Associates, Energy Prices 1960-73. Cambridge: Ballinger Publishing Company, 1975, p. 111. Henderson, Dennis R., et al., Simulating the Fertilizer Industgy, Agricultural Economics Report NO. 190, Depart- ment of Agricultural Economics, Michigan State Univer- sity, February, 1972. "National LP Gas Association, 1972 LP Gas Market Facts, 1973. Rose,Sanford. "Why Big Oil is Putting the Brakes On," Fortune, 93:110-115, 173-176, March, 1976. United States Department of Agriculture, Agricultural Prices, Statistical Reporting Service. Various reports from 1973 and 1975. CHAPTER VI CONCLUSIONS AND IMPLICATIONS OF MODEL RESULTS Problem Review The cost of energy related inputs such as fertilizer and fuels used in agricultural production have increased substantially since 1973. Without a comparable increase in output prices, farm income would have been considerably re- duced. Some crOps use fewer energy inputs than others. Corn hybrids use large amounts of natural gas derived nitrogen fertilizers and LP gas for drying purposes, while soybeans require limited nitrogen and generally no drying. As energy prices increase, the profitability Of soybeans relative to corn increases, given that soybean and corn prices remain constant. This suggests that since 1973 soybeans and short season corn hybrids, which also use less energy because of lower drying requirements, have increased in potential pro- fitability. Has this increase been enough to warrant a greater emphasis on soybean and short season corn production? Will even higher energy prices cause soybean production to increase? The Object of this study was to answer these questions. More specifically, this research analyzed (1) the Optimal crop mix that maximizes the profit of a cash grain farm in 62 63 Southeastern Michigan under current conditions, under in- creasing energy prices, and under increasing soybean prices; (2) what adjustments, if any, farmers should make to con- form with the profit maximizing crop mix for each of the conditions above; and (3) the implications on corn and soybean prices and supply responses, given that farmers make the optimal adjustments in crop mix. Review of Model Results To determine optimal crop mix an LP model was developed. The operating and environmental characteristics of a "typi- cal" farm were incorporated into the model. These character- istics included such internal and external factors as land availability, soil type, machinery components, potential crOp yields, weather conditions, labor availability, and prices. The LP model then chose the combination of corn and soybean enterprises which maximizes profits,subject to re- source constraints. Sensitivity analysis was used to deter- mine the effects On crop mix caused by (1) increasing soybean: corn price ratio, (2) increasing energy prices, and (3) poor weather conditions. This type Of analysis is accom- plished by changing prices and resource levels in the model. A summary of the model results follows. With crude Oil price at approximately $7.55 per barrel, natural gas at $0.52 per Mcf, and the soybean:corn price ratio in the 1.9:1 to 2.0:1 range, which approximates price condi- tions during the 1975 crop year and at the beginning of the 64 1976 crop year, the optimal crop mix is comprised Of 475 acres of long season corn, 17 acres of short season corn, and 107 acres of short season soybeans, or 82 percent corn. The long season corn hybrids are planted in the first three spring periods (April 20-May 19). The moisture contents are relatively high (23-30 percent). Soybeans are harvested between September 15-30, followed by corn harvest in the next three periods (October l-November l4). Ninety-two percent of the plowing occurs in the fall. Given constant energy prices and corn price, as soy- bean price increases, corn acreage decreases, operating income increases, and energy use decreases. If the constant corn price is raised to a higher level, corn acreage and energy use decrease at a lower rate. Long season, high moisture content corn hybrids planted early remain in the solution as soybean prices increase. For a given soybean:corn price ratio, as energy prices increase, soybean acreage increases at a relatively slow rate. For instance, at a ratio of 2:1, soybean acreage in- creases from 18 to 28 percent of available land while natural gas increases from $0.52 to $1.49 per Mcf and oil increases from $7.55 to $9.06 per barrel. For ratios less than 2.4:1 this lew acreage increase predominates. For a given soybean price level long season corn activities planted early remain in the Optimal solution despite substantial increases in energy prices. Depending on the soybean:corn price ratio, Operating income decreases by amounts ranging from 14-32 65 percent as energy prices increase. As expected, energy use declines as soybean acreage increases. If plowing capacity is limited by poor weather condi- tions in the fall, model results indicate that there would be little effect on income, corn acreage, or energy use. At least this is the conclusion if the soybean:corn ratio is 2:1 and weather limits plowing to 50 percent of capacity.’ Poor weather conditions that limit planting in the spring cause an increase in soybean acreage, an increase in use of short season corn hybrids, and a decrease in income. Implications on Farm Adjustments After a review of the LP model results for the various sensitivity analyses, several recommendations: can be made to the farmer producing corn and soybeans. The primary deter- minant of how much corn to plant is the soybean:corn price ratio. Long season corn and short season soybeans are the primary hybrids planted throughout the soybean price range. In general, to maximize income the farmer should plant as much as possible of the highest yielding long season corn activity (up to the acreage suggested for the given price ratio) as early as possible in the spring, subject to fall harvesting capacity constraints. Suggested soybean acreage is planted in the later Spring periods and harvested in the early fall periods. Shortseason corn hybrids are planted only when soybean acreage is less than 10 percent. Plow as much land as possible in the fall. Even though moisture 66 content may be high, harvest corn before field loss becomes significant. If poor weather conditions limit planting in the early spring periods, a switch to short season corn and an increase in soybean acreage should be made. What adjustments in crop mix should the farmer make if energy prices increase? Assume that natural gas price is de- regulated and the price increases to $1.25 per Mcf from $0.52 per Mcf. The model suggests that the percentage of land in corn decreases to 73 percent from 82 percent. If crude Oil prices are decontrolled and the average domestic price in- creases to $9.06 from $7.55 per barrel, the model results show that corn acreage remains constant. The oil price increase decreases profits, but acreages remain relatively constant. The effects of a simultaneous deregulation of Oil and natural gas prices are slightly greater than gas deregulation alone. With the soybean:corn price ratio at 2.0:1, corn acreage decreases from 82 to 72 percent as energy prices in- crease. The increased production costs cause profits to decrease. As energy prices increase, the percentage of land in corn in the optimal corp mix decreases. To determine how much to decrease corn acreage, the farm manager should translate the increase in production costs Of corn relative to soybeans into an equivalent soybean price increase. If he knows how to vary corn acreage as the soybean:corn price ratio varies, the farmer then knows how to vary corn acreage as energy prices increase . 67 The farm manager should not switch to short season corn hybrids as energy prices increase. Short season corn hybrids that can be harvested at low moisture levels are similar to soybeans because less energy is used in their production pro- cess. But because the maximum yield of short season corn hybrids is 80 percent (or less) of long season varieties, their energy savings are overshadowed by the lost revenue of lower yields. Effects of Energy Price Increases on Supply=Responses Increased energy prices affect the prices and supplies of corn and soybeans both in the short-run and long-run. Higher energy prices cause increased production of soybeans and less corn production. Supply disequilibriums cause corn price to increase and soybean price to decrease. This in turn leads to increased production of corn and decreased soybean production. Thus, there is a cycle of corn and soy- bean supply disequilibriums along with changing product prices. This cycle decreases in amplitude until the long-run supply equilibrium is reached. The increase in energy prices causes the long-run average cost curve for both corn and soy- bean production to increase. But the increase is significantly greater for corn. In the long-run the equilibrium price for both corn and soybeans is greater. If constant demand is assumed, the equilibrium supply quantities for corn and soy- beans are slightly less than the previous long-run equilibriums, 68 with corn supply decreasing by a greater amount than the soybean supply. The short-run supply fluctuations of corn and soybeans affect livestock feeding enterprises. Because corn and soy- beans have high complementarity in feeding enterprises, re- duced supplies Of one crop lead to limited consumption of the other, even if price is considerably lowered. In the short-run this complementarity makes the short-run fluctua- tions of corn and soybean supply even more pronounced, although there may be considerable modification in this conclusion because of increased export demand for the surplus crop,- increased demand for by-products such as soybean oil, an increase in the percentage of the cheaper crop used in feed- ing rations, and the possibility of only small changes in 'total feeding costs. Limited supply of one crop may lead to reduced livestock feeding and smaller supplies of meat and other livestock products. In the long-run the increase in the equilibrium prices of corn and soybeans causes production costs of livestOck products to increase. This increase in costs causes the prices of livestock products to increase. Another effect is possible. If it is assumed that poultry enterprises require less corn relative to soybeans than pork and beef feeding enterprises, increased energy prices cause the increase in poultry price to be less than pork and beef prices, which leads to increased consumption of poultry products. 69 Review of Significant Conclusions Several significant conclusions can be derived from the analysis results. They are listed below. 1. The crop mix that maximizes profits consists of long season corn hybrids planted in early spring periods and harvested at near maximum yield levels with high moisture contents and short season soy- bean hybrids. As thesoybean:corn price ratio increases, corn acreage decreases, Operating income increases, and energy use declines. Short season corn activities have limited use because their potential yield levels are low relative to other corn hybrids. As much plowing as possible should be done in the fall. When poor weather conditions limit spring planting, an increase in soybean acre- age and greater use of short season corn hybrids occurs, but operating income decreases substantially. Planting capacity during the April 20-May 9 period and harvesting capacity between October 15 and November 14 limit operating income when the soybean: corn price ratio is less than 2.5:1. The farm manager who wants to maximize his income should determine the field operation capacities in spring and fall periods for his machinery, the potential yield of his soil, and costs of production for corn and soybeans. From this information he 70 can determine how to vary corn and soybean produc- tion when input and output prices change by using various computer models supplied by agricultural extension services. The short-run result of an increase in energy prices is an increase in soybean acreage and a decrease in corn acreage, which in turn causes increased supplies of soybeans and decreased supplies of corn. To regain market equilibrium a cycle of short-run supply and price disequili- briums occurs. Eventually, equilibrium quantities stabilize at slightly smaller levels than the previous long-run corn and soybean equilibrium quantities. Equilibrium prices will be higher, if it is assumed that demand remains constant, because the long-run average total cost curves are at higher level. The changes in corn and soy- bean supply caused by increased energy prices affect livestock production. Because Of the comple- mentarity Of corn and soybeans in feeding Opera- tions, decreased supplies of one cause only a limited increase in the use of the other. If supply changes are relatively severe, the level of feeding Operations could decrease which would lead to decreased supplies of meat and other livestock products. In the long-run higher energy prices cause higher feed prices which increase livestock 71 production costs. This leads to increases in livestock product prices. Also, those livestock enterprises which require relatively smaller amounts of corn gain a price advantage over live- stock enterprises requiring large amounts of corn. Deregulation of crude oil does not change the optimal acreages of corn and soybeans. Deregula- tion of natural gas increases soybean acreage from 18 to 27 percent of total land available. For simultaneous decontrol of energy prices soybean acreage increases from 18 to 28 percent. This has the equivalent effect of a 30 cent per bushel rise in soybean price. Thus, deregulation of energy prices has a relatively minor effect on corn and soybean production. A governmental policy to reduce energy use in agriculture by de- regulating prices would do little to reduce con- sumption. But a governmental policy that restricts energy consumption would limit corn production and cause supply disequilibriums. Use of short season corn hybrids and increased field drying to reduce energy use in agriculture causes a 19 percent decrease in net income. De- creasing energy use in this manner has a great opportunity cost. But energy accounting suggests that use of the short season hybrids increases energy efficiency of agriculture, or that the 72 ratio of energy output to energy input increases. Clearly, this increase in energy efficiency is gained at the loss of economic efficiency. Limitations of This Study Several factors and alternatives which may affect or limit the applicability of the conclusiOns derived from this study should be discussed. The first factor that should be recognized is that the linear programming model is structured to look at only the direct effects of energy price increases on corn and soybean production. There are secondary effects that were not considered. For instance, as energy prices increase, an increase in general price levels may occur because the real costs of many consumer and capital goods increase. Real disposable income decreases which causes demand to decrease. Farm machinery costs increase, and, because corn is more machinery intensive, a switch to soybeans or other enterprises may result. The decrease in real income also leads to a slowdown in economic growth because of lower demand and decreased saving. Judgements concerning the full effects of an energy price increase are very difficult to make. Other factors may have some influence on the LP model results. The level of nitrogen use for the corn activities in the LP model is determined by equating the marginal cost and marginal revenue of nitrogen use, when initial conditions are assumed. As energy and corn prices change, the marginal 73 cost and marginal revenue of corn production change. These changes in MR and MC can affect the amount of nitrogen applied to the corn activities, but this effect is not con- sidered in the model. Not considering potential changes in nitrogen use biases the results toward increased soybean production. Changes in herbicide and pesticide prices as energy prices increase also are not considered. Another factor to consider is that only one technology level was examined. The LP model maximizes profit, given a specific level of technology. As energy prices increase, the farm manager might increase the use of labor relative to machinery use or switch to different production techniques. These types of adjustments were not studied. Several assumptions used to generate the LP model might affect applicability. The "typical" farm used in the model produces only corn and soybeans. In general, farms in South- eastern Michigan produce other crOps also. The model did not look at the effect of having other crop and livestock enterprises on the farm. The farm also has a relatively large machinery component. This may cause results to be biased toward corn. When the relative change in prices of energy related inputs was determined as the prices of oil and natural gas increase, only the primary relationships were considered. As energy prices increase, the costs of transportation, proces- sing, and other secondary functions increase because these 74 functions also use energy. This secondary effect was not incorporated into input costs. In the determination of how prOpane price changes as energy prices change, the assumption was used that propane varies with crude Oil price because historic price relationships indicate this fact. But other data suggest that a large percentage of propane is processed from natural gas, which makes it feasible that propane price varies with natural gas price. This price variation was not considered. Additional Useful Research A look at the limitations of this study suggests many areas where additional research is needed. An investigation of the indirect effects of energy price increases on such factors as general price levels and economic growth rates would be useful. The validity of the results of this study could be improved by also varying nitrogen, herbicide, and pesticide use as energy prices change. A study of the effects of changing technology levels as a result of energy price increases is needed. Finally, an investigation needs to be made of how much short season corn hybrid yields have to increase before these varieties become an important part of cropping combinations. APPENDICES APPENDIX A EXHIBIT A1. VERBAL DESCRIPTION OF LP MODEL STRUCTURE The LP model derived contains 131 activities (columns) and 92 constraints (rows). Columns 1-52 contain the various corn growing activites. Each activity specifiesa short, medium, or long season corn hybrid planted during a certain spring period and harvested during a specific fall period. Columns 53-61, 129-131 contain short, medium, and long season soybean hybrids planted and harvested during various spring and fall periods. Columns 62-71 are plowing activities during fall and spring periods. Columns 72-76 are harrowing activities in the five spring periods. Columns 78-81 are interperiod planting transfer activities in the spring periods. Columns 82-86 are corn harvesting activities in the fall periods. Columns 87, 88, and 128 are soybean harvesting activities. Columns 89-93 are ammonia application activities during spring periods. Column 94 is an ammonium nitrate purchase activity. Columns 95-104 are activities which hire labor for fall and spring periods. Column 105 is a sell dry corn activity. Columns 106-114 are purchase activities for labor, fuels, fertilizers, and seeds. Column 115 is a sell soybean activity. Columns 116 -124 are interperiod plowing transfer activities and columns 125-127 and 77 are interperiod harrow- ing transfer activities. The interperiod transfer activities are in the model to make sure that the tillage sequence 75 76 proceeds in the correct order. a Row 1 is a land use constraint. Row 2 is a hired labor inventory row and Row 3 is an accumulation of corn inventory. Rows 4-13 are family labor constraints for the various time periods. Rows 14-23 are field time constraints for the spring and fall periods. Rows 24-28 and.3l-35 are plowing inventory rows which allow prOper sequencing of this acti- vity. Rows 29, 30, and 67 are soybean harvest inventory rows. Row 36 is an anhydrous ammonia application inventory row. Rows 37-41 are harrowing inventory rows. Rows 42-46 are planting inventory rows and Rows 47-51 are corn harvesting inventory rows. Rows 52-56 constrain corn drying activites. Rows 57-65 are inventories of fuel, fertilizer, and seed. Row 66 is a soybean inventory row. Rows 68, 69 and 90-92 constrain harrowing activities. Rows 70-74 constrain planting activities. Rows 75-79 constrain harvesting activities and Rows 80-89 restrict fall and spring plowing. To complete the LP matrix numerical values of the various constraints must be supplied. These are commonly called right hand sides (RHS). The important values of this column are given in Table A2. Another element necessary to complete the model is the objective function row. This row gives the prices or costs of bringing an activity into solu- tion. The values of this row are presented in Table A1. EXHIBIT A2. EXAMPLE OF EQUIVALENCE OF SOYBEAN PRICE INCREASE AND AN ENERGY PRICE INCREASE An increase in energy prices is equivalent to an in- crease in the soybean:corn price ratio. This can be ex- plained in the following manner. Assume that maximum corn and soybean yields of 115 and 38 bushels, respectively, are Obtained and that corn is at $2.25 and soybeans at $4.50 per bushel. If Table A5 Of Appendix A is referred to, at present energy prices total variable cost per acre equals $102.02 for corn and $53.07 for soybeans. Gross income for corn is $258.75 and $171.00 for soybeans, which gives opera- ting incomes per acre of $156.73 and $117.93, respectively. Corn has an income advantage Of $38.80. At $2.25 per bushel for corn expected corn yield must be less than 97.75 bushels per acre before soybeans become more profitable. But what happens if natural gas increases to $1.49 per Mcf and crude oil to $9.06 per barrel, which wOuld approxi- mate energy prices if price controls are eliminated (how these prices are derived and how they affect input prices are dis- cussed in Chapter V)? The total variable cost of corn and soybeans increases to $115.01 and $54.62, respectively. Under these conditions corn has a profit advantage of $27.36 per acre, or a decrease of $11.44. If eXpected corn yield is below 103 bushels, soybeans become more profitable than corn. 77 78 This decrease in the profitability of corn can be viewed in another way. After the increase in energy prices corn is $11.44 less profitable per acre. This is equivalent to say- ing that gross revenue of soybeans has increased $11.44. 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Iacreslr ($) Leve1 (:cres)4___IS) Level (Acres) (S) land Use coo ns coo m L coo nc coo 99 Planting S! 144CL' as "3%, 13 mm 12 mo. 42 "mung sz 23ch 1c ,gggg 9 1:22;; am. . 9 ‘gljg zc Planting s: I 3:: o ascn o o o 23%: 7 Hunting so I 107535 0 134535 0 220535 0 ms 0 Hunting ss I o o o o o o o o Harvesting n f toms o msas 0 229585 0 sscs o Harvesting r2 3 “39; o czcn o zccs o ‘ggg o mmsmg r3 um 11 125cm 0 Izccn 0 ma 9 Harvesting n 3 ma 7 ma 9 140m 10 ma 5 Harvesting rs ? 33cm. 0 em 5 aw. c can. a flowing n 107 0 1c 0 7c 0 55 o Plowing n I m o no I no 2 m a flowing r: I n o I 126 o 12c o n 0 91mm; :4 I 53 0 cs 0 cs 0 47 o floating rs I 157 I 157 I 157 I 157 a flooring 51 I o o o o o o 9 o Ploflng 52 I o o c o c o 92 o "ovum; ss jI so 0 o o o o 7 o A... AppHcann 51 I o o o o L o o o 0 An. Appmmon sz I o o o o o o o o h. Appmmon $3 I 31 o o o 234 o o o AIL Appiication $4 I 263 0 0 0 0 o 69 0 An. Appmmon 55 I 199 o no 0 14c o 531 o 0c I corn 3. 0 soybeans L ' Iong season variety H - median season variety 3 - short season variety Table l5 (can‘t): 104 Activities and Constrains of the Sensitivity Analyses Analysisfgg. S 6 ., 7 Factwity TJF lcuflty WP Activfiv F‘JP Rctivity WWP Level#j}:re) {3: Levcl ’:cres) (S) Level (izres} (S) Level incres) (51 Land Use coo 99 coo 103 coo 122 cm 134 .'Planting Sl 1::CL 42 l4£CL 35 lcch 29 icch 18 Planting $2 lBlCL sscs 2c um 17 23m 1c 23611 9 Planting 53 ms 1.1m mses ZCZCL 7 lTCS O S-‘-CL O O O Planting $4 | 7C5 0 55385 0 25585 0 220585 0 Planting 55 o o o o o o o o Harvesting r1 secs 0 55535 9 mm o zzosas o Harvesting rz ‘ 144cm 1am I ms 0 nos n mu a mu 0 Harvesting n I 14m 9 113a 9 1:3a 4 143a a Harvesting n I 14m 8 mm 11 mu. 0 can. a Harvesting F5 ; 88CL 3 SSCL 3 O 0 0 O Plowing 71 I 55 o 55 o m o 99 o Plowing F2 151 o m o m n no 11 moving r: I 71 o 71 o 71 o 71 o Plowing n I 17 o 17 0 c1 0 109 0 Moving rs I 157 3 157 3 157 a 157 2 moving 51 I 9 o o o o o o o Plowing 52 I 92 0 70 o o o o 0 Moving s: I 7 o :19 o o o o 0 An. Application 51 I 11 o o o o o 37 o An. Application 52 0 O 0 0 0 0 0 0 An. Application 53 0 O 0 0 0 0 l05 0 An. Application 54 c9 0 14 o 390 o 233 0 An. Application 55 531 3 531 o 13 11 o o 5 (Can't) mm as (can‘t): ‘ 11 I 12 1-77‘ P Activity MVP Activity MVP Anal sis No. 9 ') Lelelgj::res) (5) Level (ficres (S) I. l coo 145 cm 145 Land Use _, 7 llicL 2 lIACL Z 'Planting 51 I ' 0 29d 0 29a 0 Planting s2 " 3 535m 0 535135 a - 229555 175535 Planting 53 o NGSBL 0 195m 9 Planting $4 0 O 0 0 0 71 m' n, 5‘ io 228S8S 51 1755135 96 ”mm” W A 0 1995131. 37 l99SBL 79 """m" '3. 0 mu. 0 mu 0 “man” ’- 9 29a 0 290. o Morvesting' O O o 0 0 "man”. 0 77 n 77 o "M” n A 1 70 o 70 o "M” n. o 21 o 111 o "M“, r!“ 1 117 3 117 3 Plowing u 3 157 3 157 3 "M” o o o n o "M” ~ 0 12 o 12 o "M" o as o as 0 mm. o o o o o h. MI 0 o o o o '1‘. ml 0 zc o o o h. M. o co 0 co 0 A... Mi 9 cc 0 112 o umt" 105 Table IS: Activities and Constraints of the Sensitivity Analyses (Con't) flirt“ 113: 9 I 10 11 i 12 Activity .‘WP Activity -"'.'P Activity MVP Activity MVP Level (Acre) (SI Level (.flcres) 45) LelelJAnes) (S) Level (Acres (3) Land Use coo 151 coo 141 coo 145 cm 145 Planting 51 met 9 mm. 7 ma 2 . 14451 2 Planting 52 231m 0 21451. 0 29¢: o 2911 o Planting 53 o o I o a 53531. 0 53535 0 Planting 54 225555 T 223535 223555 175535 111531. 0 l46$8L 0 195531. 0 Planting SS 0 O I 0 0 0 0 0 0 Harvesting 51 I 225535 0 : 223535 l0 223535 51 175535 95 Harvesting 1'2 111m 0 I 11551. I 154 CL 0 199531. 37 19953L 79 Harvesting 1'3 I 113a 1 f 15311 9 mm. 0 mu 0 iiel'vesting ra ‘ 33a 0 66CL o 29cc 0 29m 0 Harvesting F5 0 0 i 0 0 0 O O o Plowing 51 35 o . . 77 o 77 n 77 o Plowing 52 no 1 1 no 1 70 0 7o 0 Plowing 53 71 o . 71 o 31 o 31 o Plowing 54 117 . 1 1 117 1 117 3 117 3 Plowing 75 157 3 157 3 157 3 157 3 Plowing 51 o o 7 o o o o o Plowing $2 0 O 5 0 0 l2 0 l2 0 Plowing 53 I o o . o o 35 o 35 o A111. ApplicatiOn 51 I 55 o I o o o o o 11 A111. Application 52 i n o I o o o o o o in. Application 53 ' o o I 155 o 25 o o 0 An. Application 5.1 233 o I o o co 0 co 0 An. Application 55 9.5 o I 232 o 35 o 112 o 106 Table 85: Activities and Constraints of the Sensitivity Analyses (Con't) Analysis lio. l3 ll 15 16 — i Aafifiy WT 3::1‘v1ty "Jr activity W activity TIP LevelJAcre) 15) Level _‘L=cres) (5) Level (Acres) (5) Level IAcres) (5) Land Use 600 ii? 600 l4? 600 N7 600 142 ‘ Planting Sl Nil 0 l7CL 0 "CL 0 l54CL 55 Planting 52 0 0 0 O 0 0 55C$ 3i lBICL Planting 53 57SBL O SJSBL 0 57SBL 0 lOCS 8 ' 202CL Planting 54 223555 228535 223535 NZSBL O "6531 0 NZSBL 0 7C5 0 Planting SS 0 O O 0 (l 0 O 0 Harvesting Fl 223585 139 I 228555 181i 223565 229 SSCS 0 Harvesting F2 l99$8L i20 ll9SBL l5: l99$8L 205 lMCL 0 l7CS iiarvesting F3 l7CL 25 ”CL 36 l7CL 86 NBC. l3 Harvesting ca 0 0 0 0 0 0 "EL 6 Harvesting F5 0 0 o 0 0 o SSCL o Plowing Fl 77 O 77 O 77 0 55 0 leing F2 70 0 70 0 70 0 l6l 0 Ploving F3 53 0 53 O 53 0 7i 0 Ploving F: in 3 H7 3 H7 3 i7 0 Plowing F5 l57 J 157 3 l57 3 l5? 3 Plowing Si 65 0 6l 0 O 0 5 0 Plowing 52 37 0 28 0 9l 0 92 0 Plowing 53 23 0 36 0 35 O 7 0 A211. Application SI 0 O O 0 l7 0 0 0 An. Application 52 0 0 l7 0 0 0 0 0 ~11. Application 53 0 0 O 0 0 0 0 0 ~11. Application 51 L o o o o o o 59 0 An. Application 55 17 O O 0 O 0 5:" 0 ].()'7 Table 05: Activities and Constraints of the Sensitivity Analyses (con't.) _1 Analysis 110. 17 i 13 19 1' 20 h l’39th WV , Activity "a? Activity ‘WF 1fiTcWrity 4W Level (Acre) (Si 'LeveLL-‘ncresl 45) Level (Acres) (51 LeveLIAcres) (5) Land Use 60‘) l“ 600 l56 600 l64 600 l79 Planting Sl lMCL 53 N40. 47 N¢CL 45 l44CL 30 Planting 52 £805 l885'. 29 2360. 22 23GCL 2l 236CL l7 "m'" 5’ 155%: 5 1353 o 5533: 0 195535 a Planting 54 7555 0 55585 0 65535 0 25585 O Planting 55 o o o o o o o o Harvesting :1 :53: o I 55535 0 137535 0 220535 0 Harvesting 12 1i725 o I 1:53 0 14m 0 mm. o Harvesting F3 HEEL l7 I NECL ll NSCL l2 NBCL 6 Harvesting F4 l47CL l3 I "KL 7 NH. 6 88CL O Harvesting F5 BSCL 6 I 63CL 0 0 0 O 0 Plowing Fl 55 0 I 55 0 l37 0 85 0 Planing F2 lél 0 lEl 0 l“ 0 no 0 Moving 73 71 o 71 o 71 o 71 o Plowing 14 47 o 47 o 55 o 117 o Planing F5 l5? 3 l5? 3 l5? 3 l5? 2 Moving 51 9 o 1 53 o o o o 0 "Wing 52 92 0 O 0 0 0 0 0 Moving 53 1 o 55 o 35 o o o h. Application 51 o o o o o o .o o M. Application 52 O 0 I 0 0 0 0 fl An. Application 53 o o I o o o o o h. Application 56 62 0 l4 0 0 0 0 0 h. Application 55 531 0 SJl O 462 0 380 O 108 Table 85: Activities and Constraints of the Sensitivity Analyses (con't.) 2.9.511“! no. 21 I 22 l 23 za Activity fit? I Activity l'i‘lP Activity MVP Activity HVP Level ijcrel '(S) ’Level flares) '5) Level (Acres) (5) Level LAcres) (8) Land Use coo 113 coo 112 coo 112 coo 119 Planting 51 met 35 met 34 moi. 32 met 35 Planting 52 235a 15 235m. 15 23551. 15 23511 . 15 "mm 53 5:53 o 55:: 0 55a 0 195:: o Planting 54 I 107535 0 I 120535 0 155535 0 1117595 0 Planting 55 o o I o o o o o o Harvesting 71 107535 o I 120535 0 155535 0 107535 0 ”'"m'" '2 1m: 0 I 1115:: 0 mu 0 111%? o liarvestinn n I 14951 11 I "3“ a lasct 5 111221. 11 Harvestino M I 115a 7 met 5 ma 2 1115a 7 Harvesting F5 JRCL 0 27CL O 0 0 33:1 0 Moving Fl 137 * o 120 o 155 o 107 0 moving 52 I 152 o 151 o 1411 o 151 o Ploving 53 ' 71 o 71 o 71 o ‘ 71 0 Moving u 53 o 55 0 5a 0 53 o Plowing rs 157 l 157 2 157 3 157 1 Plowing 51 o o o o o o o o planning 52 . o o o o a o 9 o elovino 53 59 o 35 o o o 51 ' o h. Application Si 0 0 o 0 0 0 O 0 An. Application 52 o o 43 o 39 o 31 o 7111:. Application 53 31 a o o o 159 o o 11 An. Application 54 o ‘ 11 24c 11 o o 253 0 hi. Application 55 A62 0 l87 0 236 0 l” o 109 Table 85: Activities and Constraints of the Sensitive Analyses (con't.) m Activity 25 ":13 3 f-ct‘IVltv 1:511 Y Tctfiitv 27 1119 Activity 23 W!- Level (AcreL IS) ‘Levol flint-5) (S) ILevel (Acres) (S) Level (Acre_5)__L§)_ Land 11:: 500 114 500 113 300 112 500 33 Manting 51 met 35 14411 34 ' 14451. -34 14455 37 Manting 52 23551. 15 23552 15 23551. ' 15 13351. 22 Manting 53 1755625335 £55 0 53.335 3 “1&5 3 Manting 54 35535 3 707535 0 o o 7535 o Manting 55 . o o o 0 137535 3 o o 4555 liamating 51 107535 0 107535 0 ma 0 7535 o liarvctting 1'2 I 11:515. 0 1115: 0 14351 3 “515:1. 3 ‘flamsting 53 I 14351. 10 143a 15 14451. 3 14351. 3 Harvesting 53 3 14551. 7 14m 7 an 4 met 3 Harvesting F5 I JSCL 0 3351 0 0 0 ”CL. 0 Moving 51 I 157 o. 107 0 137 o 55 3 Moving 52 I 151 o I 151 o 144 o 151 0 Moving 53 I 71 o 71 o 71 o 71 o Moving 54 I 53 o 53 o 55 o 47 3 Moving 55 157 ' 1 157 l 157 2 157 Moving 51 o o o o o o 103 o Plowing 52 0 0 0 0 0 0 0 5 Moving s3 50 o 50 o 35 o o 0 An. Application 51 o o o o o o ' o o In. Application 52 0 0 0 0 0 0 0 0 An. Application 53 o o ‘o o o o o 0 An. Application 54 233 o o o o o 52 0 An. Application 55 133 o 433 o 453 o 531 o 110 table IS: Activities and Constraints of the Sensitivity Analyses (con'tl @s '30. Activity 29 F??? ktivity .‘fvl’ IT Activity WWW—3L“- lcvel itcrg (S) Leve'. (£51135) IS) Level (Acres) (S) Level (Acres) (51 Land 1155 500 134 500' 135 503 133 500 112 Manting 51 14451 13 15451 3 . 14451 3 14451 311 Manting 52 I 23551 4 22351 0 4351 0 23551. 15 Manting 53 I o o o 3 33531 0 5551 o Manting 54 I 223535 3 223535 0 32551:: 3 155535 o Manting 55 r o o o o I o 3 o o liarvesting 51 I 220535 0 223535 4 I 223535 12 155535 3 Aarvosting 52 I 14451 0 14451 0 I 173531 0 14455 3 vamsting 53 I 14351 4 14351 0 I 14551 0 14351 5 liarvastinn 54 I 3351 o 3051 o I 4351 0 14351 1 Harvesting '5 I 0 O 0 0 I 0 0 0 0 Moving 51 I 33 o 77 o I 77 o 155 0 Moving 52 I 173 o 170 1 I 113 o 144 o Moving 53 I 71 o 71 o I 31 o 71 3 Moving 54 I 154 o 117 1 ' 117 3 53 0 Moving 55 I 157 l 157 3 157 3 157 3 Moving 51 I o o o o 23 o o 3 Moving 52 o o o o 1 o o 4 0 Moving 53 o o 7 o I 25 o o 3 An. Application 51 43 o o 0 I o o o 0 An. Application 52 o o o o I 35 0 33 0 An. Application 53 o o o o I 55 o ' 153 o Ao.’ Application 54 o o 227 o 102 o 134 o An. Application 55 332 o 145 o o 0 53 o 111 13013 35. Activities and Constraints 0f the Sensitivity M31y5es (can't) 151311515 1.0. 33 z 34 35 36 "'— Actlvity WP I #:tfi-{ty f-ivP 751157111 WP :‘ctivitf—‘Wr— level (A5531 (5) 11.5731 (£5535) ISL LeveI (15535) (81 Level (At-53M” Land Use 500 93 500 133 500 133 500 135 Montinc :1 14451 34 14451 3 14451 3 14451 2 Maw 52 $32; 13 23551 1 22351 . 0 2351 o "m,“ 5; 13:1 0 o 0 o 0 53535 0 5 175535 Manting 54 7535 0 220535 0 223535 0 193531 0 flantIng $5 0 O 0 O 0 0 0 0 “mm” '1 :32; 0 220535 0 223535 7 223535 14 ”mm" '2 111g: 0 14551 0 14451 0 133531 3 Harvesting 53 _ 14351 3 14351 3 14551 0 12451 11 Harvesting 54 I 14751 3 3351 0 3351 o 4351 o limctting 55 I 3351 3 I 0 0 o o o 0 Moving 51 I 55 0 I 33 o 77 o 77 0 Moving 52 I 151 o I 170 o 170 1 7o 0 910371519 F3 I 71 0 I 71 0 79 O 130 0 Moving 54 I 47 0 104 0 117 1 ' 117 3 Moving 55 I 157 157 1 157 3 157 3 Moving 51 3 0 o 0 o o o 0 Moving 52 32 0 0 o 0 o 43 o Plowing 53 I 7 0 O 0 0 O O 0 In. App1icetion $1 0 0 I 48 0 O 0 O 0 All. Appiicetion $2 0 0 I 0 O o 0 O 0 In. AppHcAtion $3 . 0 O 0 0 159 0 - 59 0 In. Appiication St I 62 O 238 O O 0 0 O An. Application 55 531 0 -95 0 212 0 113 o 112 Table I5: Activities end Constreints of the Sensitivity Analyses (Con't.) W5 no. 37 y I 40 l Activity "'1? I Whit] VJF Activity WP fictivity W5- tevel (£33 15) 'Level fires) (5) Level izcres) 45) Level (Acres) (5L land Use 600 111' 600 97 600 131 600 I30 Planting Sl IMCL 27 144121 32 14451 7 14451 6 Planting $2 236d. 16 236d. 17 23161. 0 7051 0 Planting 53 “Cl. 176 152535 0 1‘7“ 0 0 0 IZSIS ‘ O Planting 54 14535 0 55535 0 225535 0 fig: 0 Planting SS 0 O 0 O 0 0 O 0 Harvesting '1 166585 0 55535 0 225585 0 228535 10 “WNW '2 "“3- ° 11% 0 14451 0 113:: o Harvesting F3 "BEL 3 "ML I 1180. 2 145CL 0 Harvesting 1’4 142CL 0 N7“ 6 ”Cl. 0 6961. O \ Harvesting 55 o 0 I 3351 3 0 0 0 0 ' Moving 51 155 o I 55 o 35 0 77 0 Moving 52 144 0 I 151 o 170 1 170 0 Plowing F3 71 O I 71 0 7l 0 79 0 Plowing H 61 0 I 47 0 117 l 117 1 "Owing F5 l57 3 157 J 157 2 157 3 Moving 51 0 0 o 0 0 0 0 o Plowing $2 0 0 $3 0 0 0 0 0 Plowing $3 0 0 55 0 0 0 0 0 All. Applicetion $1 0 0 I O 0 39 0 O O 7.. Application $2 0 0 I 0 0 0 O 18 0 An. Application 53 0 0 I 0 0 102 0 0 0 An. Application 54 330 0 I 14 0 233 0 117 0 All. Application 55 43 0 I 531 0 0 0 78 O 113 Table 55: Activities and Constraints 01' the Sensitivity Analyses (Con‘t.) Em 74217177111 41 1.") 5:113? ‘2 RV; ktWity “ P junk; “ VIP Level (Acre) (5) Level (acres) 1;) - Level (Acres) 18) Level flares) (3) Land use 500 132 505 113 500 115 500 113 Planting 51 144m 2 144:1 34 14451 35 0 35 Planting 52 251:1 0 mm 15 mm. 15 23551 20 Planting 53 213555 0 11751 0 3:: 0 £35; 4 Planting 54 135:: 0 103555 0 107555 0 151555 0 Planting 55 0 0 o 0 o 0 o 0 151-vesting 51 225555 17 103555 0 I 107555 0 151555 0 iumsiing 52 155551. 5 13m 0 111:1? 0 130c5 0 I Harvesting 53 1 124m 0 1:50. 12 145a 3 14551 5 Harvesting 54 1 45a 0 14511 1 I mu 0 15ch 5 ‘liarvesting 55 0 o 55c1 0 I 41:1. 0 27c1. 0 Moving 51 I 77 o 55 5 I 107 o 111 0 Moving 52 I 70 o 55 3 I 151 o 170 0 Moving 53 L 130 0 55 3 I 71 o 71 0 Moving 54 I 117 3 50 o I 55 5 55 0 Moving 55 I 157 3 75 - 4 I o o 157 2 Moving 51 I o 0 75 0 I 51 0 o 0 Moving 52 45 0 55 o I 35 o 1 0 Moving 53 o 0 55 o I 55 0 35 o h. Application 51 O 0 O 0 I O O O 0 An. Application 52 0 0 o. 0 I 0 0 o o in. Application 53 o 0 _ o 0 0 0 0 0 h. Application 54 0 O 269 0 263 0 0 0 in. Application 55 173 0 225 0 230 0 445 0 114 Table 85. Activities and Constraints of ti-e Sensitivity Analyses (Con't.) WrisWNo. . if . 55 47 fl IF - ’w Activity I??? 1 Activity T415 Activity WP ktivitflfl" Level (Acre) LS) =Level (Acres) (51 Level LAcres) (5) Level (Acres) IS) Land Use 500 105 500 113 . 500 40 500 113 Planting 51 72c1. 43 14451 25 . me; 23 14451. 15 Planting 52 115c1. 37 235a. 17 I 23513. 5 ‘ 23551. 10 Planting 53 I 107:1. 15 I 223% o I ”SI-$22” 5 205555 0 Planting 54 I "gig; 0 I 135555 0 I 214555 0 14555 0 Planting 55 I o o I 0 o I 35555 0 0 o Harvesting 51 I 225555 3 I 155555 0 3 225555 0 220555 0 iiimsoing 52 I I: I“; o I ma 0 fmufsiggs 3 144:1. o llaflnting 53 I 14555 0 I 14511 2 E 145m. 14 14501 2 liarvasting 55 I 5051. 0 I 14311 2 I um 13 55a 0 Jiarvesting 55 I o 0 I 0 0 I 5.551 51 o 0 Moving 51 77 o I 155 0 I 55 0 55 0 Moving 52 170 1 I 144 o I 55 o 170 0 Moving 53 1 75 0 I 71 0 I 71 0 55 0 Moving 54 I 117 1 I 55 0 I 47 0 117 0 Moving 55 157 2 I 157 3 I 157 21 157 2 Moving 51 0 0 I o o I 135 0 o 0 Moving 52 0 0 I 0 0 52 o 0 0 Moving 53 o o I 4 o 55 15 0 o in. Application 51 1 0 o I 0 o 0 o o 0 An. Application 52 35 o I o o o 0 o 0 in. Application 53 151 0 I 152 o 0 o 0 0 An. Application 54 0 0 ' o 0 125 0 0 0 in. Application 55 153 o 272 0 415 0 350 o 115 Table 86: Listinq of Specific Activities in flptimal Solution *l. 6-144, 9-l7, l6-l48, 28-50, 31-95, 43-39, 57-107. N 0 5-4, 8-59, 15-90, 18-36, 25-52, 28-88, 40-88, 57-184. (A) 0 7-26, 15-126, 25-56, 28-84, 40-88, 57-220. 4:. 3-55, 6-144, 9-10, 10-7, l6-93, 19-55, 31-147, 43-88. same as 4. 6. 6-144, 9-17, 16-148, 31-147, 43-83, 57-55. 7. 6-144, 16-148, 28-88, 31-54, 54-142, 57-25. 8. 6-144, 16-148, 28-88, 57-220. 9. 6-144, 16-148, 28-83, 57-225. 10. 6-144, 16-148, 28-66, 57-228, 58-14. 11. 13-144, 28-29, 55-53, 57-228. 12. 13-144, 28-29, 54-53, 57-175, 58-l?”. 13.' 25-17, 55-57, 57-228, 58-142, 129-156. 14. Same as l3. 15. Same as l3. 16. 3-55, 6-144, 9-10, 10-7, 16-93, 19-55, 31-147, 43-88. 17. 3-48, 6-144, 9-17, 16-180, 19-48, 31-147, 43-88, 57-7. 18. 6-144, 9-17, 16-148, 31-147, 43-88, 57-55. 19. 6-144, 16-148, 28-61, 31-83, 43-27, 54-72, 57-65. 20. 6-144, 16-148, 28-88, 54-195, 57-25. 21. 6-144, 9-17, 16-148, 28-50, 31-95, 43-38, 57-107. 22. 6-144, 9-17, 16-148, 28-61, 3l-83, 43-27, 57-120. 23. 6-144, 16-148, 28-88, 31-55, 57-165. 24. 6-144, 9-17. 16-148, 28-50, 31-95, 43-38, 57-107. 25. Same as 24. 26. Same as 24. *Listinq is by analysis number. First number is activity number. The acreage of the activity follows. Activities 1-52 are corn and activities 53-61 and 129-131 are soybeans. 116 Table 36. Listing of Specific Activities in Optimal Solution (con't.) 27. 28. 29. 30. 31. 32. 6-144, 16-148, 28-61, 31-83, 43-27, 54-50, 57-87. 3-48, 6-144, 9-17, 16-100, 19-48, 31-147, 43-88, 57-7. 6-144, 16-148, 28-88, 57-220. 6-144, 16-148, 28-80, 57-223. 13-144, 28-49, 55-33, 57-228, 58-146. 6-144, 16-148, 28-88, 31-55, 57-165. 3-48, 6-154, 9-17, 16-100, 10-48, 31-147, 43-98, 57-7. 6-144, 16-148, 28-88, 57-220. 6-144, 16-145, 28-83, 57-228. 13-12d, 25-20, 28-29, 54-53, 57-175, 58-109. 6-144, 16-148, 28-83, 31-54, 54-152, 57-14. 6-144, 9-17, 16-148, 31-147, 43-88, 57-55. . .5-144, 16-148, 28-83, 57-225. 13-144, 16-1, 28-69, 55-12, 57-228, 58-146. 13-124, 25-20, 28-29, 54-213, 57-15, 58-199. 6-144, 16-148, 28-29, 31-117, 43-59, 57-103. 6-144, 9-17, 16-148, 28-47, 31-95, 43-41, 57-107. 9-130, 16-148, 28-61, 31-83, 57-151. 6-72, 10-75, 16-118, 19-27, 31-80, 57-228. 6-144, 16—148, 28-88, 31-55, 54-26, 57-139. 6-1d4, 9-13, 16-148, 31-147, 41-88, 54-11, 57-214, 60-35. 6-144, 16-148, 28-88, 54-206, 57-14. 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