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 $20x_1 + 30x_2 + 10x_3 + 15x_4$ s.t. $5x_1 + 7x_2 + 12x_3 + 11x_4 \le 21$ (Constraint 1) $x_1 + x_2 + x_3 + x_4 \ge 2$ (Constraint 2) $x_1 + x_2 \le 1$ (Constraint 3) $x_1 + x_3 \ge 1$ (Constraint 4) $x_2 = x_4$ (Constraint 5) $x_j = \begin{cases} 1, & \text{if location j is selected} \\ 0, & \text{otherwise} \end{cases}$ Solve this problem to optimality and answer the following questions: a. Which of the warehouse locations will/will not be selected? Location 1 will Location 2 will Location 3 will Location 4 will

          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 $20x_1 + 30x_2 + 10x_3 + 15x_4$
s.t. $5x_1 + 7x_2 + 12x_3 + 11x_4 \le 21$ (Constraint 1)
$x_1 + x_2 + x_3 + x_4 \ge 2$ (Constraint 2)
$x_1 + x_2 \le 1$ (Constraint 3)
$x_1 + x_3 \ge 1$ (Constraint 4)
$x_2 = x_4$ (Constraint 5)
$x_j = \begin{cases} 1, & \text{if location j is selected} \\ 0, & \text{otherwise} \end{cases}$
Solve this problem to optimality and answer the following questions:
a. Which of the warehouse locations will/will not be selected?
Location 1 will
Location 2 will
Location 3 will
Location 4 will

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)
xj = 1, if location j is selected
0, otherwise
Solve this problem to optimality and answer the following questions:
a. Which of the warehouse locations will/will not be selected?
Location 1 will
Location 2 will
Location 3 will
Location 4 will

Added by Kim W.

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