Problem $4($Healthcare Resource Planning$)15$ points

A local laboratory that performs five different nontraditional tests is planning to offer a new diagnostic test for

regional hospitals. The manager assessed the current required staff and analyzer times, as well as the chemical

materials required for a bundle of $50$ vials for each type of test, as shown in the following table.

$($a$)$ Formulate the problem as an optimization model and solve it to provide an optimal resource allocation, i$.$e$.,$

which tests should be offered?

$($b$)$ What is total expected profit from the new tests?

$($c$)$ Which resources should be expanded?

$($d$)$ How much additional revenue can be expected if the resources are selected in part $($c$)$ for expansion without

violating the current solution?

Note: you may need to use the Python$-$Gurobi interface or Excel Solver for this question.

I II III IV V Available

Resources

Profit $($$$)8108710$

Staff $($minutes$)15151520253400$

Auto Analyzer Equipment

$($minutes$)$

$20404060456000$

Materials $12151614142700$