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

Quizplus · Accepted Answer

Constraint 1 (5x1 + 7x2 + 12x3 + 11x4 ≤ 21) directly limits the total spending on the new warehouses by setting a maximum combined cost, ensuring the firm does not exceed its available capital.

A Firm Has Prepared the Following Binary Integer Program to Evaluate