A firm has prepared the following binary integer program to evaluate a number of potential new capital projects. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital.
Max 100x1 + 120x2 + 90x3 + 135x4
s.t. 150x1 + 200x2 + 225x3 + 175x4 ? 500 {Constraint 1}
X1 + x2 + x3 + x4 ? 2 {Constraint 2}
X2 + x4 ? 1 {Constraint 3}
X2 + x3 ? 1 {Constraint 4}
X1 = x4 {Constraint 5} $$x _ { j } = \left\{ \begin{array} { l }
1 , \text { if project } j \text { is selected } \
0 , \text { otherwise }
\end{array} \right.$$
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 new capital projects. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital.
Max 100x1 + 120x2 + 90x3 + 135x4
s.t. 150x1 + 200x2 + 225x3 + 175x4 ? 500 {Constraint 1}
X1 + x2 + x3 + x4 ? 2 {Constraint 2}
X2 + x4 ? 1 {Constraint 3}
X2 + x3 ? 1 {Constraint 4}
X1 = x4 {Constraint 5} $$x _ { j } = \left\{ \begin{array} { l } 
1 , \text { if project } j \text { is selected } \
0 , \text { otherwise }
\end{array} \right.$$
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 (X2 + x4 ≤ 1) enforces a mutually exclusive relationship because it implies that at most one of the projects 2 or 4 can be selected, not both.

A Firm Has Prepared the Following Binary Integer Program to Evaluate