Igor Yeltsin operated a farm under the former Russian collective farm system. The collective farm-raised hogs for distribution by the central government as its main activity. Previously, Igor was told how many hogs to raise each year by Moscows central planning agency and was allocated the necessary animal feed to raise the hogs. With the new market-driven economy, Igor receives no instructions on how to operate his hog farm and must survive as best he can on his own by buying animal feed, raising hogs, and selling them to any buyers he can find. Hogs were fed a combination of corn and potatoes mixed to assure that minimum amounts of two primary nutrients were met: crude protein and calories. Corn and potato supplies have become less certain, and Igor has contracted to buy waste food scraps from a nearby food processing plant to supplement the previous hog diet of corn and potatoes. Igor has turned to you, a recently arrived United Nations consultant, for help in managing his farm in the new and very uncertain Russian market economy. On his own, Igor contracted to sell up to 100 hogs to a Moscow butcher in the next month for a fixed price of 450 rubles per hog. In addition, Igor contracted to buy up to 800 kilograms of waste food from the processing plant for a price of 10 rubles per kilogram. He believes he can buy any amount of corn for 19 rubles per kilogram and can purchase up to 600 kilograms of potatoes from a nearby potato farm for 15 rubles per kilogram. The table below presents the monthly requirements per hog in units of protein and thousands of calories (i.e. Kilo-calories). It also presents, for the three sources of animal feed, the amount of crude protein and Kilo-calories supplied per kilogram.

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CHART 2 ^

3. I think I can persuade the butcher to buy another 5 hogs from me at the same 450 ruble price. Would my situation improve if I try to sell him 105 hogs instead of 100? By how much would my operating income be improved, if at all? asks Igor. (5 points)

4. You have to understand that everything is very volatile just now. Igor comments. For example, it could easily happen that the cost of the corn that I buy might suddenly change. How much could the cost of corn increase before I would have to change my plans? (4 points)

(Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$19 Decisions Hogs Sold 100.000 0 450 1E+30 261.048 $C$19 Decisions Corn purchased 95.238 0 -19 1.917 1 $D$19 Decisions Food scraped purchased 742.857 0 -10 0.5 24.694 $E$19 Decisions Potatoes purchased 600.000 0 -15 1E+30 1.095 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $F$22 Hogs supply limit LHS 100 261.048 100 5.405 21.739 $F$23 Food scraped supply limit LHS 742.857 0 800 1E+30 57.143 $F$24 Potatoes supply limit LHS 600 1.095 600 166.667 109.091 $F$25 Crude Protein Net Excess Nutrients LHS 0 -1.048 0 46800 1500 $F$26 Kilo-Calories Net Excess Nutrients LHS 0 -0.005 0 6000 78000)

THIS IS SHOWN IN THE CHART 2 ^

MINIMUM REQUIREMENT AMT. SUPPLIED AMT. SUPPLIED AMT. SUPPLIED PER HOG PER PER KILOGRAM PER KILOGRAM PER KILOGRAM MONTH OF CORN OF FOOD WASTE OF POTATOES NUTRIENT Crude Protein Kilo-calories 18 174 1400 30 120 80 To help Igor understand how to run his farm, another United Nations consultant has built the following LP algebraic formulation and its corresponding Excel model: "Yeltsin.xlsx" (posted on the course website below the link of assignment #2) H= number of Hogs Sold C= Corn Purchased (in kg) F= Food scraped Purchased (in kg) P=Potatoes purchased (in kg) Objective function: Maximize net revenue=450H-19C-10F-15P Subject to: H= 174H (amount of crude protein) 30C+120F+80P>= 1400 H (amount of kilo-calories) H, C, F, P>=0 Food Corn scraped Potatoes Hogs Sold purchased purchased purchased 100.000 95.238 742.857 600.000 $450.00 $19.00 -$10.00 $15.00 26,761.90 Decisions Price Constraints: Hogs supply limit Food scraned sunny limit Food scraped supply limit Potatoes supply limit Crude Protein Net Excess Nutrients Kilo-Calories Net Excess Nutrients LHS 100 742.857 600 0 0 9 -174 -14001 18 30 15 80 120 >=1 The Excel model above shown displays the optimum answer to maximize Igor's operating income. The corresponding solver Sensitivity Report is also presented: Igor has many questions to ask about operating his farm, which you will expertly answer by examining the Sensitivity Report and/or the Excel solver output provided above. Variable Cells Reduced Cost Cell Name $B$19 Decisions Hogs Sold $C$19 Decisions Corn purchased $D$19 Decisions Food scraped purchased $E$19 Decisions Potatoes purchased Final Value 100.000 95.238 742.857 600.000 0 0 0 0 Objective Allowable Coefficient Increase 450 1 E+30 -19 1.917 - 100 . 5 -15 1 E+30 Allowable Decrease 261.048 1 24.694 1.095 Constraints Cell Name $F$22 Hogs supply limit LHS $F$23 Food scraped supply limit LHS $F$24 Potatoes supply limit LHS $F$25 Crude Protein Net Excess Nutrients LHS $F$26 Kilo-Calories Net Excess Nutrients LHS Final Value 100 742.857 600 Shadow Constraint Allowable Price R.H. Side Increase 2 61.048 100 5.405 0 800 1 E+30 1.095 600 166.667 -1.048 0 46800 -0.005 O 6000 Allowable Decrease 21.739 57.143 109.091 1500 78000 0 Some of Igor's questions cannot be answered from the Solver information given on the previous page. If so, answer as best you can from the information, state why a more detailed answer is not available, and if appropriate, modify the "Yeltsin.xlsx model posted on the course website below the link of assignment #2 and rerun Solver to produce the answers he seeks. MINIMUM REQUIREMENT AMT. SUPPLIED AMT. SUPPLIED AMT. SUPPLIED PER HOG PER PER KILOGRAM PER KILOGRAM PER KILOGRAM MONTH OF CORN OF FOOD WASTE OF POTATOES NUTRIENT Crude Protein Kilo-calories 18 174 1400 30 120 80 To help Igor understand how to run his farm, another United Nations consultant has built the following LP algebraic formulation and its corresponding Excel model: "Yeltsin.xlsx" (posted on the course website below the link of assignment #2) H= number of Hogs Sold C= Corn Purchased (in kg) F= Food scraped Purchased (in kg) P=Potatoes purchased (in kg) Objective function: Maximize net revenue=450H-19C-10F-15P Subject to: H= 174H (amount of crude protein) 30C+120F+80P>= 1400 H (amount of kilo-calories) H, C, F, P>=0 Food Corn scraped Potatoes Hogs Sold purchased purchased purchased 100.000 95.238 742.857 600.000 $450.00 $19.00 -$10.00 $15.00 26,761.90 Decisions Price Constraints: Hogs supply limit Food scraned sunny limit Food scraped supply limit Potatoes supply limit Crude Protein Net Excess Nutrients Kilo-Calories Net Excess Nutrients LHS 100 742.857 600 0 0 9 -174 -14001 18 30 15 80 120 >=1 The Excel model above shown displays the optimum answer to maximize Igor's operating income. The corresponding solver Sensitivity Report is also presented: Igor has many questions to ask about operating his farm, which you will expertly answer by examining the Sensitivity Report and/or the Excel solver output provided above. Variable Cells Reduced Cost Cell Name $B$19 Decisions Hogs Sold $C$19 Decisions Corn purchased $D$19 Decisions Food scraped purchased $E$19 Decisions Potatoes purchased Final Value 100.000 95.238 742.857 600.000 0 0 0 0 Objective Allowable Coefficient Increase 450 1 E+30 -19 1.917 - 100 . 5 -15 1 E+30 Allowable Decrease 261.048 1 24.694 1.095 Constraints Cell Name $F$22 Hogs supply limit LHS $F$23 Food scraped supply limit LHS $F$24 Potatoes supply limit LHS $F$25 Crude Protein Net Excess Nutrients LHS $F$26 Kilo-Calories Net Excess Nutrients LHS Final Value 100 742.857 600 Shadow Constraint Allowable Price R.H. Side Increase 2 61.048 100 5.405 0 800 1 E+30 1.095 600 166.667 -1.048 0 46800 -0.005 O 6000 Allowable Decrease 21.739 57.143 109.091 1500 78000 0 Some of Igor's questions cannot be answered from the Solver information given on the previous page. If so, answer as best you can from the information, state why a more detailed answer is not available, and if appropriate, modify the "Yeltsin.xlsx model posted on the course website below the link of assignment #2 and rerun Solver to produce the answers he seeks