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# Linear Programming - Sensitivity Analysis

2. Igor Bender 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 Moscow's 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 as 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 ensure that minimum amounts of two primary nutrients were met: crude protein and calories. Corn and potato suppliers 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, and the supply per kilogram of the same for the three sources of animal feed.

Nutrient Minimum Requirement per Hog per Month Amount Supplied per Kilogram of Corn Amount Supplied per Kilogram of Waste Amount Supplied per Kilogram of Potatoes
Crude Protein 174 18 9 15
Kilo-calories 1400 30 120 80

To help Igor understand how to run his farm, build and solve the linear programming problem, perform sensitivity analysis, and present him with a report. In particular be sure to answer the following questions which were posed to you by Igor in a recent conversation:
? How much money can I make from this farm? How many hogs will I sell, and how much corn, potatoes, and food scraps should I buy now?
? I think I can persuade the butcher to buy another 5 hogs from me at the same 450 ruble price. Would it improve my situation?
? Everything is very volatile now. For example, it could easily happen that the cost of the corn might suddenly change. How would such a change affect my plans?
? Business relationships are really uncertain in Russia just now. I am nervous that the farm manager selling me the potatoes will not honor his promise to deliver the 600 kilograms. If he delivers only 500 kilograms of potatoes, how much will I be hurt? What should my new strategy be?
? Are there alternate ways for me achieve the same income involving different operating strategies?
? An international salesman from the Hubert Farnsworth Company stopped by the farm and wants to sell me prepackaged dry hog feed imported from Poland. He wants to charge me 16 rubles per kilogram for the packaged hog food, which includes transportation from Poland. He says each kilogram of his product provides 16 units of crude protein and 150 kilocalories. Should I start importing hog feed from Poland?

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