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 mutually exclusive 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 mutually exclusive relationship?
A) Constraint 1
B) Constraint 2
C) Constraint 3
D) Constraint 4
E) Constraint 5

Quizplus · Accepted Answer

Constraint 3 (X1 + x2 ≤ 1) enforces a mutually exclusive relationship because it ensures that at most one of the two locations (either location 1 or location 2) can be selected, but not both.

A Firm Has Prepared the Following Binary Integer Program to Evaluate