In a linear programming problem involving two decision variables, a change in one of their coefficients in the objective function will:
A) always change the optimal solution.
B) change the feasible region.
C) never change the optimal solution because the other coefficient is still fixed.
D) change the optimal solution only if the slope of the objective function's contour changes significantly.
E) necessarily change all shadow prices.

Question

Quizplus · Accepted Answer

A change in the coefficient of one decision variable in the objective function will generally change the slope of the objective function's contour, which can in turn affect the optimal solution. However, the magnitude of this change and its impact on the optimal solution will depend on the specific values of the coefficients and the constraints in the problem. So, a change in one coefficient will only change the optimal solution if the slope of the objective function's contour changes significantly.

In a Linear Programming Problem Involving Two Decision Variables, a Change