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Unformatted text preview: Exercise 4 A farmer is planning his spring planting. He has 20 hectares on which he can plant a combination of sweetcorn, courgettes, and potatoes. 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 limited supply. The following table summarizes the data for the problem. Profit/hectare Yield/hectare Maximum Demand Irrigation Fertilizer Crop (USD) (kg) (kg) (m/hectare) (kg/hectare) Sweetcorn 2,100 21,000 200,000 2 500 Courgette 900 10,000 180,000 3 400 Potato 1,050 3,500 80,000 1 300 The following LP model of this problem has been formulated. X 1 = hectares of sweetcorn X 2 = hectares of courgette X 3 = hectares of potato max 2100 X 1 + 900 X 2 + 1050 X 3 (total profit, USD) subject to 21000 X 1 ≤ 200000 (constraint 1) 10000 X 2 ≤ 180000 (constraint 2) 3500 X 3 ≤ 80000 (constraint 3) 2 X 1 + 3 X 2 + X 3 ≤ 50 (constraint 4) 500 X 1 + 400 X 2 + 300 X 3 ≤ 8000 (constraint 5) X 1 + X 2 +...
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 Spring '10
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