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Consider the following LP: minz = 4x +4x+6x3 subject to x + 2x + 2x3 4 3x + x2 + 12x3 6 Xx +

Consider the following LP: minz = 4x +4x+6x3 subject to x + 2x + 2x3  4 3x + x2 + 12x3  6 Xx + x + x3  10 X1, 

Consider the following LP: minz = 4x +4x+6x3 subject to x + 2x + 2x3 4 3x + x2 + 12x3 6 Xx + x + x3 10 X1, X2, X30 a) Show that the basis (X2, X3, S3) is an optimal basis for the above problem and find the optimal solution. b) Write the dual of the above LP. c) Using complementary slackness, find the optimal solution of the dual problem. d) Show that strong duality holds

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