The optimal combination of decision variables of a linear programming problem is x = 20 and y = 30. The given resource constraints are: 5x + 2y ≤ 150 and y ≥ 15. The shadow price of the second constraint is:
A) 1.5.
B).67.
C) Zero.
D) 10.
E) There is insufficient information to provide and answer.

Question

Quizplus · Accepted Answer

The shadow price of a constraint in linear programming indicates how much the objective function value would change with a one-unit increase in the right-hand side of the constraint. If a constraint is not binding (meaning it does not directly limit the optimal solution), its shadow price is zero. Since the optimal solution given is x = 20 and y = 30, and the second constraint is y ≥ 15, this constraint is not binding at the optimal solution (because y = 30 is well above the minimum of 15). Therefore, the shadow price for this constraint is zero.

The Optimal Combination of Decision Variables of a Linear Programming