It can be shown that the optimal solution to following LP is z=8.67, x1 = 4.67, x2 = 0, x3 = 0. 67.

a)  Find the dual of the problem.

b)  Using the given optimal primal solution and the Theorem of Complementary Slackness, Find the optimal solution to the dual of the problem.

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Max z = 2x1 + x2 – X3 Subject to X1 + x2 + 2x3<6 x1 + 4x2 – x3 < 4 X1, X2, X3 2 0 Max z = 2x1 + x2 – X3 Subject to X1 + x2 + 2x3<6 x1 + 4x2 – x3 < 4 X1, X2, X3 2 0