WK Qu$.10-01$ A firm has prepared the following binary...

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 $20x_1+20x_2+15x_3+30x_4$

$s.t.9x_1+7x_2+13x_3+5x_{4}19\{$ Constraint $1\}$

$x_1+x_2+x_3+x_{4}2\{$ Constraint $2\}$

$x_1+x_{2}1\{$ Constraint $3\}$

$x_1+x_{3}1\{$ Constraint $4\}$

$x_2=x_4\{$ Constraint $5\}$

$x_j=\{\begin{array}{ccc}1,& if\text{l}\text{o}\text{c}\text{a}\text{t}\text{i}\text{o}\text{n}jis\text{s}\text{e}\text{l}\text{e}\text{c}\text{t}\text{e}\text{d}& \end{array}$

$0,$ otherwise

Solve this problem to optimality and answer the following questions:

a$.$ Which of the warehouse locations will$/$will not be selected?

b$.$ What is the net present value of the optimal solution?

c$.$ How much of the available capital will be spent $($Hint: Constraint $1$ enforces the available capital limit$)?$