A firm has prepared the following binary integer program to evaluate a number of potential new capital projects. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital.

Max $100$x$1+120$x$2+90$x$3+135$x$4$

s$.$t$.150$x$1+200$x$2+225$x$3+175$x$4<=500\{$Constraint $1\}$

x$1+$ x$2+$ x$3+$ x$4>=2\{$Constraint $2\}$

x$2+$ x$4<=1\{$Constraint $3\}$

x$2+$ x$3>=1\{$Constraint $4\}$

x$1=$ x$4\{$Constraint $5\}$

image

Set up the problem in Excel and find the optimal solution. Which projects are selected?

Question $8$ options:

Project $1$

Project $2$

Project $4$

Projects $2$ and $3$

Projects $1$ and $3$