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} $$x _ { j } = \left\{ \begin{array} { l }
1 , \text { if loaction } j \text { is selected } \
0 , \text { otherwise }
\end{array} \right.$$
Which of the constraints ensures that at least two of the potential sites will be selected?
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} $$x _ { j } = \left\{ \begin{array} { l } 
1 , \text { if loaction } j \text { is selected } \
0 , \text { otherwise }
\end{array} \right.$$
Which of the constraints ensures that at least two of the potential sites will be selected?
A) Constraint 1
B) Constraint 2
C) Constraint 3
D) Constraint 4
E) Constraint 5

Quizplus · Accepted Answer

Constraint 2 (X1 + x2 + x3 + x4 ≥ 2) ensures that at least two of the potential sites will be selected because it requires the sum of the variables (each representing a potential site being selected) to be at least 2.

A Firm Has Prepared the Following Binary Integer Program to Evaluate