A pharmaceutical company sells four drugs with an annual revenue generated from each drug as a function of the number of salespeople assigned to the drug. It costs the company $50,000 per year per salesperson. The revenue per drug is given in the table below where Si is the number of salespeople assigned to drug i and the revenue is expressed in thousands of dollars. The hiring budget is limited to $1.9 million. Drug-1Revenue = 200S1^{.5} ,Drug-2 Revenue=150S2^{.75} , Drug-3 Revenue= 180S3^{.6}, Drug-4 Revenue = 300S4^{.3}
a) Formulate a mathematical model to maximize the company’s profit. Clearly define your decision variables, objective function and constraints.
b) Implement your model in Excel and use Solver to find the optimal number of salespeople. Include a snapshot of your solution in the report.