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  3. maximize z s t 8x1 4x2 x1 4x1 x1 2x2 3x2 382 6x3 3

Maximize z s t 8X1 4X2 X1 4X1 X1 2x2 3x2 382 6x3 3x3 2x3...

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Basic Math

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Maximize z s t 8X1 4X2 X1 4X1 X1 2x2 3x2 382 6x3 3x3 2x3 3x4 3x4 X4 X4 9x5 180 X5 270 3x5 180 resource 1 resource 2 resource 3 Xj 0 j 1 2 3 4 5 It is known that the basic variables in the optimal solution are X3 X1 X5 a Using this information please identify the optimal solution decision variables and t optimal z value using the formulas for computing the optimal tableau from the initial LP i Section 6 2 of the textbook entitled Some Important Formulas 10 points b Find the dual of this LP 10 points c Determine shadow prices for the three resources using Dual Theorem 10 points d Let c4 be the coefficient of x4 in the objective function given above Using the Du Theorem please determine for what values of c4 will the current basis remain optimal points

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