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 constraint ensures that the firm will not spend more capital than it has available (assume that each potential project has a different cost)?
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 constraint ensures that the firm will not spend more capital than it has available (assume that each potential project has a different cost)?
A) Constraint 1
B) Constraint 2
C) Constraint 3
D) Constraint 4
E) Constraint 5

Quizplus · Accepted Answer

Constraint 1 directly limits the total spending on projects to not exceed the available capital of 500, by summing the costs of selected projects and ensuring this sum does not surpass the capital limit.

A Firm Has Prepared the Following Binary Integer Program to Evaluate