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$1+30$ x$2+10$x$3+15$x$4$

s$.$t$.5$x$1+7$x$2+12$x$3+11$x$4<=21\{$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 $5\}$

xj$=\{1,$ 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?

What is the net present value of the optimal solution?

Note: Round your answer to the nearest whole number.

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

Note: Round your answer to the nearest whole number.