Problem 2. Non-linear Optimization (9 points)

A pharmaceutical company RxCorp has four products in the market. The company is interested in optimizing its overall sales force size and its allocation to the four products in its portfolio. Based on studies from its consultants, it was shown that product sales have the following relationship with sales force headcount:

where S is the product sales (in million dollars), R is the number of sales representatives assigned to a product, a, b, c and D are parameters. The consultant also provided the following table for the parameters for the four products along with the gross margin information for next year 2022:

	a	D	b	c	Gross margin %	Base case # of reps (R)
Product 1	30	120	2.01	5600	70%	80
Product 2	20	70	2.56	2500	55%	40
Product 3	14	40	2.3	450	72%	50
Product 4	12	35	3.04	520	70%	25

Question 2.1 [2 points] (Base Case Plan Evaluation)

Use the above information to predict the overall sales and profit (=sales x gross margin % sales force cost) assuming sales reps cost $150,000 per person for the base case plan for the year 2022 depicted in the last column in the above table.