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Ops Mgmt Midterm solutions

# Ops Mgmt Midterm solutions - 0.12 X 12 0.25 X 22 ≤ 0.15 F...

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Q1: Solution (note that text to the right side of constraint is not part of the standard solution). Decision Variables: X ij = Number of Pounds of Raw Material i (i=1,2) that is mixed into Fertilizer j (j=1,2,3), Y = Amount (\$) spent on Advertising. Helpers F j = Number of Pounds of Fertilizer j produced, j=1,2,3. Ri = Number of Pounds of Raw Material i=1,2, used, Maximize (8-1.5) F 1 + (6-1.2) F 2 + (7-1) F 3 – 3 R 1 – 2 R 2 – Y (Profit = Revenue - Cost) S.T. F 1 = X 11 + X 21, F 2 = X 12 + X 22 , F 3 = X 13 + X 23 . R 1 = X 11 + X 12 + X 13 , R 2 = X 21 + X 22 + X 23 0.3 X 11 + 0.1 X 21 ≥ 0.25 F 1 (Nitrogen in Fertilizer 1) 0.3 X 12 + 0.1 X 22 ≥ 0.2 F 2 (Nitrogen in Fertilizer 2) 0.3 X 13 + 0.1 X 23 = 0.15 F 3 (Nitrogen in Fertilizer 3) 0.12 X 11 + 0.25 X 21 = 0.18 F 1 (Phosphorus in Fertilizer 1)

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Unformatted text preview: 0.12 X 12 + 0.25 X 22 ≤ 0.15 F 2 (Phosphorus in Fertilizer 2) 0.12 X 13 + 0.25 X 23 ≥ 0.2 F 3 (Phosphorus in Fertilizer 3) 0.15 X 11 + 0.25 X 21 ≤ 0.2 F 1 (Potassium in Fertilizer 1) 0.15 X 12 + 0.25 X 22 = 0.2 F 2 (Potassium in Fertilizer 2) 0.15 X 13 + 0.25 X 23 ≤ 0.22 F 3 (Potassium in Fertilizer 3) F 1 ≤ 250 + Y, F 1 ≤ 250 + 100 (Demand for Fertilizer 1) F 2 ≤ 300 + 2 Y, F 2 ≤ 300 + 120 (Demand for Fertilizer 2) F 3 ≤ 150 + Y, F 3 ≤ 150 + 200 (Demand for Fertilizer 3) R 1 ≤ 800 (Available Raw Materials) R 2 ≤ 600 3 R 1 + 2 R 2 + 1.5 F 1 + 1.2 F 2 + F 3 + Y ≤ 6,000 (Budget) Y ≥ 0, X ij ≥ 0, i=1,2; j=1,2,3....
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Ops Mgmt Midterm solutions - 0.12 X 12 0.25 X 22 ≤ 0.15 F...

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