Question: 4. (20%) While solving a standard form linear programming problem, we arrive at the following simplex tableau. Z X1 X X3 X4 X5 X6 RHS

4. (20%) While solving a standard form linear

4. (20%) While solving a standard form linear programming problem, we arrive at the following simplex tableau. Z X1 X X3 X4 X5 X6 RHS 1 h i 0 0 3 0 0 4 d 1 0 e 0 -1 0 -5 0 1 0 -1 2 0 -3 0 -4 0 1 3 g1 The entries d, e, f, g, h, i are unknown parameters. For each one of the following statements, find the parameter values that will make the statement true. (a) The current solution is optimal and an alternative solution exists, provided that d > 0. (b) The current solution is feasible but the problem is unbounded. (c) The current solution is a degenerate basic feasible solution. (d) The current solution is feasible and the objective value can be improved by replacing X6 by X1. What will the change in the objective value be after the pivot? 2

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