The shadow price for a constraint that expresses that the availability of wood is 3000 board-feet is $0.50, and the range of feasibility is between 2800 and 4000 board-feet.Which of the following is not correct?
A)All 3000 board-feet of wood will be used.
B)If only 2900 board-feet of wood are available, the optimal objective function value will be reduced by $50.
C)If only 2900 board-feet of wood are available, the optimal solution will not change.
D)If 6000 board-feet of wood are available, the objective function value will increase by at least $500.

Question

Quizplus · Accepted Answer

The shadow price of $0.50 means that for every additional board-foot of wood available, the optimal objective function value will increase by $0.50. The range of feasibility suggests that if less than 2800 or more than 4000 board-feet of wood are available, the problem is infeasible.

Option A is correct because all 3000 board-feet of wood will be used because it is feasible and is at the optimal point.

Option B is correct because if there is a reduction in the availability of wood to 2900 board-feet, then it is below the current value of 3000 board-feet, therefore the optimal objective function value will be reduced by $0.50 * (3000 - 2900) = $50.

Option D is correct because if there is an increase in the availability of wood to 6000 board-feet, then the increase in the objective function will be at least $0.50 * (6000 - 3000) = $1500.

The Shadow Price for a Constraint That Expresses That the Availability