All of the following are true about a variable with a negative reduced cost in a maximization problem except
A)its objective function coefficient must increase by that amount in order to enter the basis.
B)it is at its simple lower bound.
C)it has surplus resources.
D)the objective function value will decrease by that value if the variable is increased by one unit.

Question

Quizplus · Accepted Answer

A variable with a negative reduced cost in a maximization problem implies that the objective function value can be increased by that amount if the variable enters the basis. Therefore, option A is true. Option B is false because if the variable is at its simple lower bound, then it cannot be increased further, hence its reduced cost cannot be negative. Similarly, option C is false because if the variable has surplus resources, then it can be increased without violating any constraints, hence its reduced cost cannot be negative. Option D is true because the objective function value will decrease by an amount equal to the reduced cost if the variable is increased by one unit.

All of the Following Are True About a Variable with a Negative