An analyst, having solved a linear programming problem, determined that he had 10 more units of resource Q than previously believed. Upon modifying his program, he observed that the optimal solution did not change, but the value of the objective function increased by $30. This means that resource's Q's shadow price was:
A) $1.50.
B) $3.00.
C) $6.00.
D) $15.00.
E) $30.00.

Question

Quizplus · Accepted Answer

Since the optimal solution did not change when the analyst added 10 more units of resource Q, it means that the problem was not resource Q-constrained before. Therefore, the shadow price of resource Q is the amount of increase in the objective function value divided by the amount of increase in resource Q.

In this case, the objective function value increased by $30 when 10 more units of resource Q became available. Therefore, the shadow price of resource Q is:

Shadow price = ($30 increase in objective function value) / (10 increase in resource Q) = $3.

Therefore, the correct answer is B.

An Analyst, Having Solved a Linear Programming Problem, Determined That