A Blending Problem

1. A Blending Problem COSC643 Dr. Sungchul Hong

2. 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.

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

4. 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.

5. 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.

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

7. 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