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Pharmadex sells four drugs

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


Drug 1 200S10.5
Drug 2 150S20.75
Drug 3 180S¬¬30.6
Drug 4 300S40.3

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

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Solution Preview

Please see attached files.

a. Let Si be the number of salespeople for drug i.
Let Ci be the cost for drug i.
Let Ri be the revenue for drug i. Ri can be calculated using Table 1.
Let Pi be the profit for drug i.
We need to maximize the following function:

I have done so in Excel using the Solver tool. Note that ...

Solution Summary

The solution provides step-by-step instructions and calculations required in Word and Excel files. It also include Solver code in Excel.