Question: Consider the linear programming problem: Minimizing z = -8x1 - 4x2 - 23 - 1524 subject to 3 1 + 202 + 223 + 4x4

Consider the linear programming problem: Minimizing z = -8x1 - 4x2 - 23 - 1524 subject to 3 1 + 202 + 223 + 4x4 + 2'5 = 14 8x1 + 2x2 - 23 + 724 + 26 = 25 1 , . . . , 26 2 0. Given the initial and final Simplex tableau: x1 X2 X3 x4 x5 x6 x5 3 2 4 O 14 X6 8 N -1 7 O 25 -8 -4 -1 -15 O O 0 Final: x4 -2 O 5 N -1 3 x2 11 -18 O - 7 4 N 6 2 0 2 53 (1). Find B, B-1, CB. (2). Find A* , b* , 20, and the optimal value. (3). Assume that the coefficient for x1 in the objective is changed into -8 + 1. Find the range of > such that the optimal solution is unchanged and/or remains feasible. (4) Find the optimal value Zmin . Give reason. Hint: useful formulas: A* = B-! A, b* = Bulb, c* = c - CBB A, zo = Zo - CBB b

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