A maximizing linear programming problem with constraints C1, C2, and C3 has been solved. The dual values associated with the problem are C1 = $2, C2 = $0.50, and C3 = $0. Which statement below is false?
A) One more unit of the resource in C1 would add $2 to the objective function value.
B) One more unit of the resource in C2 would add one more unit each of X and Y.
C) The resource in C3 has not been used up.
D) The resources in C1 and in C2, but not in C3, are scarce.
E) The resource in C2 must be used up first.

Question

Quizplus · Accepted Answer

EB) This statement is false because the dual value represents the change in the objective function value per unit increase in the resource, not the change in decision variables like X and Y.E) This statement is false because the dual value indicates the marginal worth of the resource. A dual value of $0.50 for C2 does not imply it must be used up first; it simply means each additional unit of this resource adds $0.50 to the objective value. The order of resource usage is not determined by dual values alone.

A Maximizing Linear Programming Problem with Constraints C1, C2, and C3