Real Estate Project Selection. Brooks Development Corporation $($BDC$)$ faces the following capital budgeting decision. Six real estate projects are available for investment. The net present value and expenditures required for each project $($in millions of dollars$)$ are as follows:

Project

$1$

$2$

$3$

$4$

$5$

$6$

Net Present Value $($$ Millions$)$

$$15$

$$5$

$$13$

$$14$

$$20$

$$9$

Expenditure Required $($$ Millions$)$

$$90$

$$34$

$$81$

$$70$

$$114$

$$50$

There are conditions that limit the investment alternatives:

At least two of projects $1,3,5,$ and $6$ must be undertaken.

If either project $3$ or $5$ is undertaken, they must both be undertaken.

Project $4$ cannot be undertaken unless both projects $1$ and $3$ also are undertaken.

The budget for this investment period is $$220$ million.LO $2,$ LO $4,$ LO $5,$ LO $7$

a$.$Formulate a binary integer program that will enable BDC to find the projects to invest in to maximize net present value, while satisfying all project restrictions and not exceeding the budget.

b$.$Solve the model formulated in part $($a$).$ What is the optimal net present value? Which projects will be undertaken? How much of the budget is unused?