A farmer is planning his spring planting. He has 20 acres on which he can plant a combination of Corn, Pumpkins and Beans. He wants to maximize his profit but there is a limited demand for each crop. Each crop also requires fertilizer and irrigation water which are in short supply. There are only 50 acre ft of irrigation available and only 8,000 pounds of fertilizer available. The following table summarizes the data for the problem.

Formulate the linear programming model (mathematical formulation) for this problem.

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Profit per Yield per Acre (Ib) Irrigation (acre ft) Fertilizer Crop Maximum Demand (Ib) Acre (S) (pounds/acre) 200,000 Corn 2,100 2 21,000 500 3 Pumpkin 900 10,000 180,000 400 3,500 80,000 Beans 1,050 300