Suppose that the optimal values of the decision variables to a two-variable linear programming problem remain the same as long as the slope of the objective function lies between the slopes of the following two constraints: 2X1 + 3X2

Question

Suppose that the optimal values of the decision variables to a two-variable linear programming problem remain the same as long as the slope of the objective function lies between the slopes of the following two constraints: 2X1 + 3X2 < 26
2X1 + 2X2 < 20
The current objective function is:
8X1 + 9X2 = Z
Which of the following statements about the range of optimality on c1 is TRUE?
A)0 < c1 < 2
B)2 < c1 < 6
C)6 < c1 < 9
D)9 < c1 < 12

Quizplus · Accepted Answer

The slope of the objective function (c1/c2) must lie between the slopes of the constraints. The slopes of the constraints are -2/3 and -1. The slope of the current objective function is -8/9. For the optimal solution to remain unchanged, the slope of the objective function must be between -2/3 and -1, which corresponds to 6 < c1 < 9 when c2 is 9.

Suppose That the Optimal Values of the Decision Variables to a Two-Variable