# Dual formulation

May 13th, 2015
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Final dictionary of primal (verified by tableau obtained by simplex solver), Z = 10.5 – 1.5 x3 – 2 x4 – 0.5 x5. X2 = 1.5 – 0.5 x3 – x4 + 0.5 x5

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Exercise of Lecture 55.a.Dual formulation:Min 4 y1 + 5 y2 + 7 y3 Subject to, y1 + 2 y2 + 2 y3 3y1 + 0 y2 + y3 22 y1 + 3 y2 + 3 y3 4 y1, y2, y3 0Final dictionary of primal (verified by tableau obtained by simplex solver), Z = 10.5 1.5 x3 2 x4 0.5 x5. X2 = 1.5 0.5 x3 x4 + 0.5 x5X1 = 1 1.5 x3 0.5 x5X6 = 0.5 + 0.5 x3 + x4 + 0.5 x5We see that in the optimal dictionary for primal, the slack variables have coefficients: -2 at x4, -0.5 at x5, 0 at x6 Then by applying , we obtain, y1 = 2, y2 = 0.5, y3 = 0Check optimality

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