2. Linear Programming (20 points) Agri-Pro is a company that sells agricultural products to farmers in...

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2. Linear Programming (20 points) Agri-Pro is a company that sells agricultural products to farmers in a number of provinces. One service that it provides to customers is custom feed mixing, for which a farmer can order a specific amount of livestock feed and specify the amount of corn, grain, and minerals that the feed should contain. This is an important service because the proper feed for various farm animals changes regularly depending upon the weather, and pasture conditions, for example. Agri- Pro stocks bulk amounts of four types of feeds that it can mix to meet a given customer's specifications. The following table summarizes the four feeds; their composition of corn, grain, and minerals; and the cost per kilogram for each feed type: Nutrient Corn Grain Minerals Cost per kilogram Percent of Nutrient Feed 1 Feed 2 Feed 3 Feed 4 20% 15% 20% 10% 25% 30% 25% 15% 30% 20% 20% 30% $0.25 $0.30 $0.32 $0.15 Agri-Pro has just received an order from a local chicken farmer for 8,000 kilograms of feed. The farmer wants the feed to contain at least 20% corn; at least 15% grain; and at least 15% minerals. 1) Develop the model in Excel. (10 points) 2) Solve the problem of finding the least-cost feed mix. Show the Answer Report and the optimal solution. (4 points) 3) Create a Sensitivity Report and answer the following questions: a. Suppose we forced Feed 3 to be in the solution, what would happen to the objective function's value? (2 points) b. What do the shadow prices for the Corn and Grain constraints mean? (4 points) 2. Linear Programming (20 points) Agri-Pro is a company that sells agricultural products to farmers in a number of provinces. One service that it provides to customers is custom feed mixing, for which a farmer can order a specific amount of livestock feed and specify the amount of corn, grain, and minerals that the feed should contain. This is an important service because the proper feed for various farm animals changes regularly depending upon the weather, and pasture conditions, for example. Agri- Pro stocks bulk amounts of four types of feeds that it can mix to meet a given customer's specifications. The following table summarizes the four feeds; their composition of corn, grain, and minerals; and the cost per kilogram for each feed type: Nutrient Corn Grain Minerals Cost per kilogram Percent of Nutrient Feed 1 Feed 2 Feed 3 Feed 4 20% 15% 20% 10% 25% 30% 25% 15% 30% 20% 20% 30% $0.25 $0.30 $0.32 $0.15 Agri-Pro has just received an order from a local chicken farmer for 8,000 kilograms of feed. The farmer wants the feed to contain at least 20% corn; at least 15% grain; and at least 15% minerals. 1) Develop the model in Excel. (10 points) 2) Solve the problem of finding the least-cost feed mix. Show the Answer Report and the optimal solution. (4 points) 3) Create a Sensitivity Report and answer the following questions: a. Suppose we forced Feed 3 to be in the solution, what would happen to the objective function's value? (2 points) b. What do the shadow prices for the Corn and Grain constraints mean? (4 points)