Managers of Tom Brown Distributors are evaluating the compensation system for the company’s sales personnel. Currently, the two salespeople have a combined salary of  $50,000 per year and earn a 4% sales commission.

The company is considering two alternatives to the current compensation system. The first alternative is to reduce total salaries to $20,000 and increase the sales commission to 5%. The second alternative  is to eliminate the salaries and pay a 25% sales commission.

Sales projections under each of the compensation systems are as follows:

Current system                      . . . . . . . . . . . . . .     $900,000

Salary and 5% commission . . . . . . . . . . . . . . . $1,100,000

25% commission                . . . . . . . . . . . . . . .   $1,300,000 

Required

a. Write the cost equations for the current compensation system and both alternative compensation  structures.

b. Given Tom Brown’s sales projections, and assuming that the cost of goods sold is equal to 30% of  sales, which pay system would be the most profitable one for the company? Ignore all other costs  and show your calculations.