The Texas Electronics Company $($TEC$)$ is contemplating a research and development program encompassing eight major projects. The company is constrained from embarking on all projects by the number of available scientists $(40)$ and the budget available for projects $($$$300,000).$ Following are the resource requirements and the estimated profit for each project:

Project Expense

$($$$000)$ Scientists Profit $($$$000)$

$160736$

$2110982$

$353829$

$447416$

$592756$

$685661$

$773848$

$865541$

a$.$ What is the maximum profit, and which projects should be selected?

$$199\mathrm{.}00$

P$2,$ P$5,$ P$6$

b$.$ Suppose that management decides that projects $2$ and $5$ are mutually exclusive. That is$,$ TEC should not undertake both. As a result, what are the revised project portfolio and the revised maximum profit?

$$195\mathrm{.}00$

P$1,$ P$2,$ P$3,$ P$7$