A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital.
Max 20x1 + 30x2 + 10x3 + 15x4
s.t. 5x1 + 7x2 + 12x3 + 11x4 ? 21 {Constraint 1}
X1 + x2 + x3 + x4 ? 2 {Constraint 2}
X1 + x2 ? 1 {Constraint 3}
X1 + x3 ? 1 {Constraint 4}
X2 = x4 {Constraint 5} $$x _ { j } = \left\{ \begin{array} { l }
1 , \text { if location } j \text { is selected } \
0 , \text { otherwise }
\end{array} \right.$$
Which of the constraints enforces a contingent relationship?
A) Constraint 1
B) Constraint 2
C) Constraint 3
D) Constraint 4
E) Constraint 5

Question

A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital.
Max 20x1 + 30x2 + 10x3 + 15x4
s.t. 5x1 + 7x2 + 12x3 + 11x4 ? 21 {Constraint 1}
X1 + x2 + x3 + x4 ? 2 {Constraint 2}
X1 + x2 ? 1 {Constraint 3}
X1 + x3 ? 1 {Constraint 4}
X2 = x4 {Constraint 5} $$x _ { j } = \left\{ \begin{array} { l } 
1 , \text { if location } j \text { is selected } \
0 , \text { otherwise }
\end{array} \right.$$
Which of the constraints enforces a contingent relationship?
A) Constraint 1
B) Constraint 2
C) Constraint 3
D) Constraint 4
E) Constraint 5

Quizplus · Accepted Answer

Constraint 5 enforces a contingent relationship because it requires that the decision to select location 2 is directly tied to the decision to select location 4, meaning they must either both be selected or both not be selected.

A Firm Has Prepared the Following Binary Integer Program to Evaluate