Answer Happy

Consider the linear programming problem: Minimizing z = -8x14x2x3 - 15x4 subject to 3x1 + x2 + 2x3 + 4x4 + 25 = 14 8x12x2 3 + 74 www + 6 = 25 1,62 0. Given the initial and final Simplex tableau: x1 x2 x3 x5 x5 3 1 2 1 x6 8 2 -1 0 -8 -4 -1 0 Final: x4 -2 0 5 x2 11 1 -18 x4 4 7 -15 1 0 2 -7 x6 0 1 O -1 st 4 14 25 0 3 2
+26 = 25 x5 1 0 0 *1,,26 ≥ 0. Given the initial and final Simplex tableau: x1 x2 x3 x4 x5 3 1 2 4 x6 8 2 -1 7 -8 -4 -1 -15 Final: x4 -2 0 5 1 2 3 x2 11 1 -18 0 -7 2 6 0 2 0 2 1 53 Assume that the constant vector in the constraint is changed to (14+ A, 25 + X). find the range of A such that the optimal solution still uses 2, 4 as basic variables. In this case, also find the min in terms of X. Hint: useful formulas: A* = B¹A, b* = B-¹b, c = c - CBB¹A, z = 20 - CBB-¹b. x6 0 1 O -1 4 14 25 0