Develop an appropriate nonlinear optimization model

Question

Discussion:

Q. Pharmadex sells four drugs. It costs Pharmadex $50,000 per year per salesperson. The annual revenue generated from each drug is a function of the number of salespeople assigned to the drug. This dependence is shown in the table below, where Si is the number of salespeople assigned to drug i , and revenue is expressed in thousands of dollars. If Pharmadex wants to maximize profit (revenue from sales minus salesperson costs), how many salespeople should it assign to each drug?

Table Revenue Functions For Pharmadex Example

Revenue

Drug 1 200S₁^0.5

Drug 2 150S2₀^.75

Drug 3 180S¬¬₃^0.6

Drug 4 300S₄^0.3

a. Develop an appropriate nonlinear optimization model and solve it using Solver.

b. Discuss how the company might have obtained the revenue functions given in the table.