A section of output from The Management Scientist is shown here. What will happen to the solution if the objective function coefficient for variable 1 decreases by 20?
A)Nothing.The values of the decision variables, the dual prices, and the objective function will all remain the same.
B)The value of the objective function will change, but the values of the decision variables and the dual prices will remain the same.
C)The same decision variables will be positive, but their values, the objective function value, and the dual prices will change.
D)The problem will need to be resolved to find the new optimal solution and dual price.

Question

A section of output from The Management Scientist is shown here.  What will happen to the solution if the objective function coefficient for variable 1 decreases by 20?
A)Nothing.The values of the decision variables, the dual prices, and the objective function will all remain the same. 
B)The value of the objective function will change, but the values of the decision variables and the dual prices will remain the same. 
C)The same decision variables will be positive, but their values, the objective function value, and the dual prices will change. 
D)The problem will need to be resolved to find the new optimal solution and dual price.

Quizplus · Accepted Answer

If the objective function coefficient for variable 1 decreases by 20, the objective function value will change. However, the values of the decision variables and the dual prices will remain the same because the optimal solution and dual prices are determined by the constraints and the coefficients of the objective function relative to each other, not their absolute values.

A Section of Output from the Management Scientist Is Shown