3/9/2017
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• Change the objective function. • If the objective of the primal model is to maximize, then the objective of the dual model will be to minimize.
• Change the place of resource values with the objective function coefficients. • The resource values become the objective function coefficients while the objective function coefficients become the resource values.
• Take the transpose of primal model constraint coefficients. • The transpose of the primal model constraint coefficients will be the dual model constraint coefficients.
• Reverse the inequality signs.
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3/9/2017
Find the dual for the following linear programming model: Maximize: Z = 15X1 + 20X2 Subject to: 4X1 + 5X2 ≤ 100 12X1 + 8X2 ≤ 200 X1, X2 ≥ 0
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Minimize: Z = 100Y1 + 200Y2 Subject to: 4Y1 + 12Y2 ≥ 15 4
5Y1 + 8Y2 ≥ 20 Y1, Y2 ≥ 0 3
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