Assume that the shadow price of a non-binding "≤" constraint is 5.This implies that:
A)if the right-hand side value of the constraint increases by 1 unit,the objective function value will increase by 5 units
B)if the right-hand side value of the constraint increases by 1 unit,the objective function value will decrease by 5 units
C)if the right-hand side value of the constraint increases by 1 unit,the objective function value will remain unchanged
D)if the right-hand side value of the constraint decreases by 1 unit,the objective function value will increase by 5 units
E)if the objective function coefficient increases by 1 unit,the shadow price will increase by 5 units

Question

Quizplus · Accepted Answer

A non-binding constraint means that the current solution already satisfies the constraint, and an increase in the right-hand side value will still keep the constraint non-binding. Therefore, the shadow price has no effect on the objective function value, and an increase in the right-hand side value will not change the current solution. Thus, the correct answer is C: if the right-hand side value of the constraint increases by 1 unit, the objective function value will remain unchanged.

Assume That the Shadow Price of a Non-Binding "≤" Constraint