Question

Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis, each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with a maximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weekly salary is $900.

The weekly paycheck amount for each salesman, p, is a function of the number of sales, s, they had in that week.

What is the slope of the function representing the weekly paycheck amount for Salesman A? Use complete sentences to explain your reasoning, or show your calculations.
What is the slope of the function representing the weekly paycheck amount for Salesman B? Use complete sentences to explain your reasoning, or show your calculations.
What is the slope of the function representing the weekly paycheck amount for Salesman C? Use complete sentences to explain your reasoning, or show your calculations.

Answer 1

1) Salesman A:

He earns $65 per sale, with a maximum weekly commission of $1,300.

=> p(s) = 65s / p ≤ $1,300. This is the paycheck (p) equal 65 times the number of sales s, with an upper bound of $1,300.

The slope of the function is the coefficient of the the indepent variable s, this is 65.

The slope is the rate of change on the paycheck per unit of sales done (s).

Answer: slope 65.

2) Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale.

p(s) = $300 + 40s

The slope is 40 (the coefficient of the independent variable).

Again, the slope is the increase in the paycheck per unit of sale (s) performed.

Answer: slope = 40

3) Salesman C does not earn any commission. His weekly salary is $900.

p(s) = $900

It turns out that really the paycheck of this salesman is not a function of the number of sales. His/her paycheck is constant. That means that the paycheck does not change with the number of sales, and so the slope is 0.

The function is a horizontal line (slope 0).

Answer: slope 0