$2.(15$ Points$)$ Riesemberg Medical Devices is allocating next year's budget among its divisions. As a result, the

R&D Division needs to determine which R&D projects to fund. Each project requires various software and

hardware and consulting expenses, along with internal human resources. A budget allocation of

$$1,300,000$ has been approved, and $35$ engineers are available to work on the projects. The R&D group

has determined that at most one of projects $1$ and $2$ should be pursued, and that if project $4$ is chosen,

then project $2$ must also be chosen. Develop a model to select the best projects within the budget.

$($Formulate the mathematical model and solve it in Excel$)$

Project NPV Internal Engineers Additional Costs

$1$ $$400,000\mathrm{.}004$ $$196,000\mathrm{.}00$

$2$ $$520,000\mathrm{.}006$ $$400,000\mathrm{.}00$

$3$ $$430,000\mathrm{.}007$ $$70,000\mathrm{.}00$

$4$ $$600,000\mathrm{.}0012$ $$180,000\mathrm{.}00$

$5$ $$780,000\mathrm{.}009$ $$225,000\mathrm{.}00$

$6$ $$705,000\mathrm{.}0012$ $$200,000\mathrm{.}00$

$7$ $$240,000\mathrm{.}008$$$130,000\mathrm{.}00$