Selecting Projects. 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 budget available for projects $($$$300,000).$ Following are the resource requirements and the estimated profit for each project: P$1$ P$2$ P$3$ P$4$ P$5$ P$6$ P$7$ P$8$ Expense $($$$000)8582988972837788$ Profit $($$$000)6332793871656474$ Engineers $59596667$ a$.$ What is the maximum profit, and which projects should be selected? b$.$ Suppose that management decides that projects $7$ and $8$ are mutually exclusive. $($In other words, TEC will not undertake both$).$ What is the revised project portfolio and the revised maximum profit? c$.$ Suppose that management also decides to undertake at least three of projects $1-4.$ As a result, what are the revised project portfolio and maximum profit? $($Assume b$.$ is also true$)$ You only need to submit a write$-$up for part c$.($You should submit an Excel solution for all three parts$).$ Hint: In Excel, create different tabs for part a$.,$ b$,$ and c$..$ Solve independently of each other.