Question

Carter Cadillac pays commission to its car sales staff. They are paid a percent of the profit the dealership makes on the car, not on the selling price of the car. If the profit is under $500, the commission rate is 18%. If the profit is at least $500 and less than or equal to $2,000, the commission rate is 24% of the profit. If the profit is above $2,000, the rate is 27% of the profit. If p represents the profit, express the commission c(p) algebraically as a split function.

Answer 1

Answer: c(p)= 0.18 p when
`0 \leq p < 500`

0.24 p when
`500 \leq p \leq 2000`

0.27 p when
`p \geq 2000`

Explanation:

If p is the profit then and from the question we can relate as:

The 18% commission is for profits under $500

The 24% commission is for profits from $500 to $2,000

The 27% commission is for profits above $2,000

So, in terms of p, c(p) is given as:

c(p)= 0.18 p when
`0 \leq p < 500`

0.24 p when
`500 \leq p \leq 2000`

0.27 p when
`p \geq 2000`