A Blending Problem COSC643 Dr. Sungchul Hong

Agri-Pro Agri-Pro is a company that sells agricultural products to farmers in a number of states. One service it provides to customer is custom feed mixing, whereby a farmer can order a specific amount of livestock feed and specify the amount of corn, grain, and minerals the feed should contain. This is an important service because the proper feed for various farm animals changes regularly depending on the weather, pasture conditions, and so on.

Agri-Pro Agri-Pro stocks bulk amounts of four types of feeds that it can mix to meet a given customer’s specifications.

Agri-Pro Agri-Pro has just received an order from a local chicken farmer for 8,000 pounds of feed. The farmer wants this feed to contain at least 20% corn, 15% grain, and 15% minerals.

Formulation X1 = amount of feed 1 in thousands of pounds to use in the mix. X2 = amount of feed 2 in thousands of pounds to use in the mix. X3 = amount of feed 3 in thousands of pounds to use in the mix. X4 = amount of feed 4 in thousands of pounds to use in the mix.

Objective Function MIN: 250X1 + 300X2 + 320X3 + 150X4

Constratint X1 + X2 + X3 + X4 = 8 (0.30X1 + 0.05X2 + 0.20X3 +0.10X4)/8 >= 0.20 Min % of corn required (0.10X1 + 0.30X2 + 0.15X3 + 0.10X4)/8 >= 0.15 Min % of grain required (0.20X1 + 0.20X2 + 0.20X3 + 0.30X4)/8 >= 0.15 Min % of minerals required X1, X2, X3, X4 >= 0