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Simplex Method and Reduced Costs, Duality and Marginal Costs Frédéric Giroire FG Simplex 1/17 ** Simplex Method and Reduced Costs, Strong Duality Theorem ** FG Simplex 2/17 Simplex - Reminder Start with a problem written under the standard form. Maximize 5x + 4x + 3x 1 2 3 Subject to : 2x + 3x + x ≤ 5 1 2 3 4x + x + 2x ≤ 11 1 2 3 3x + 4x + 2x ≤ 8 1 2 3 x1,x2,x3 ≥ 0. FG Simplex 3/17 Simplex - Reminder Write the Dictionary: x4 = 5 − 2x1 − 3x2 − x3 x5 = 11 − 4x1 − x2 − 2x3 x6 = 8 − 3x1 − 4x2 − 2x3 z = 5x1 + 4x2 + 3x3. Basic variables: x4,x5,x6, variables on the left. Non-basic variable: x ,x ,x , variables on the right. 1 2 3 Adictionary is feasible if a feasible solution is obtained by setting all non-basic variables to 0. FG Simplex 4/17
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