Item$7$

$12$points

Time Remaining $2$ hours $43$ minutes $53$ seconds

$02$:$43$:$53$

eBook

Item $7$

Time Remaining $2$ hours $43$ minutes $53$ seconds

$02$:$43$:$53$

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 $20$x$1+20$x$2+15$x$3+30$x$4$

s$.$t$.9$x$1+7$x$2+13$x$3+5$x$419\{$Constraint $1\}$

x$1+$ x$2+$ x$3+$ x$42\{$Constraint $2\}$

x$1+$ x$21\{$Constraint $3\}$

x$1+$ x$31\{$Constraint $4\}$

x$2=$ x$4\{$Constraint $5\}$

xj$=\{1,$if$$location$$j$$is$$selected$0,$otherwisexj$=1,$if$$location$$j$$is$$selected$0,$otherwise

Solve this problem to optimality and answer the following questions:

$$

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