Selecting Projects $(20$ points$)$

A sustainable energy company is planning on a strategic development program consisting of eight potential research projects. Each project has certain resource requirements and estimated profit, summarized in the following table:

Project

Expense

$($$$000)$

Researchers

Required

Profit $($$$000)$

$1$

$60$

$7$

$36$

$2$

$110$

$9$

$82$

$3$

$53$

$8$

$29$

$4$

$47$

$4$

$16$

$5$

$92$

$7$

$56$

$6$

$85$

$6$

$61$

$7$

$73$

$8$

$48$

$8$

$65$

$5$

$41$

The number of available researchers for this development program is $40,$ and the total R&D budget is $$300,000.$ The company aims to maximize profitability by choosing the research projects.

What is the maximum profit, and which projects should be selected? $(10$ points$).$

Suppose that the company decides that if project $2$ is selected, project $8$ should also be selected. What are the revised project portfolio and the revised maximum profit? $(5$ points$)$

Suppose that the company also decides $($in addition to the requirement in $2))$ to undertake at least two of the projects involving consumer products. $($These happen to be projects $5-8).$ As a result, what are the revised project portfolio and the revised maximum profit? $(5$ points$)$

what is the answer? and what is the easy step by step way to solve on excel?