A regional laboratory that performs nontraditional tests is planning to offer new diagnostic tests for regional hospitals. Current analyzers and staff can perform these tests. The laboratory manager assessed the required staff and analyzer times, as well as the chemical materials required for a bundle of $50$ vials for each type of test listed in Table below.Question $5[20$ points$]$: A regional laboratory that performs nontraditional tests is planning to offer new

diagnostic tests for regional hospitals. Current analyzers and staff can perform these tests. The laboratory

manager assessed the required staff and analyzer times, as well as the chemical materials required for a

bundle of $50$ vials for each type of test listed in Table below.

a$.$ Formulate this as a linear programming problem.

b$.$ Solve the problem using computer$-$based linear programming software $($Excel$).$

c$.$ For the optimal solution, in terms of profit, which test$($s$)$ should be offered?

d$.$ What is the optimal volume$($s$)?$

e$.$ What is the total expected profit from the new tests?

f$.$ Which resources should be expanded?

g$.$ How much additional revenue can be expected if the resources are selected in $"f"$ for expansion without

violating the current solution?