Question

The salespeople at a local car dealership are paid a commission based on the profit earned from each car they sell. If the profit is less than $900, the salesperson gets 15% of the profit as commission. If the profit on the car is equal to or between $900 and $1,500, the salesperson gets 17% of the profit. Even better, if the profit on the car sold is more than $1,500, the salesperson gets 21% of the profit as commission. Write a function that relates the commission earned by a salesperson, C(p), to the profit earned on the car, p.

Answer 1

Hi !

In this case, C is a piecewise linear function :
 
$C : p \mapsto \begin{cases} 0.15p \text{ if } p \ \textless \ 900 \\ 0.17p \text{ if } 900 \leq p \ \textless \ 1,500\\ 0.21p \text{ if } p \geq 1,500 \end{cases}$