$(20$pt$)$ A company considers the following $4$ projects:

The MARR is $10\%$ per year. The company has a $$20,000$ budget for the capital investment in year $0.$

a$)(10$pt$)$ Find NPVs of $4$ Projects, formulate a binary integer programming problem to select

projects that maximize the total NPV$,$ and determine which projects the company should select

by solving the problem with the Excel solver.

b$)(5$pt$)$ In addition to the budget constraint, we further assume that the total cash flow in year $1$

must be nonnegative. Formulate a binary integer programming problem to select projects that

maximize the total NPV$,$ and determine which projects the company should select by solving the

problem with the Excel solver.

c$)(5$pt$)$ In addition to the constraints in $b),$ we further assume that Project $C$ can be chosen only if

Project $D$ has been selected and that Projects $B$ and $C$ are mutually exclusive. Formulate a binary

integer programming problem to select projects that maximize the total NPV$,$ and determine

which projects the company should select by solving the problem with the Excel solver.