Question

The barber’s profit each week depends on his charge c per haircut. It is modeled by p = -200c2 + 2400c – 4700. What is the reasonable domain of this function, given this situation?

Answer 1

the real answer is

`2.5 \leqslant c \leqslant 9.5`

Answer 2

0 ≤ c ≤ 12

Explanation:

The function can be rearranged to ...

p = 200c(12 -c) -4700

suggesting that revenue will be zero for a charge of 0 or for a charge of 12, and that fixed expenses are 4700. Charges less than 0 are uninteresting, and charges high enough to cause the number of customers to be negative also don't make any sense in this context.

Though out of the range of likely consideration, charges low or high enough to cause profit to be negative (more than 9.54, for example) seemingly can be reasonably modeled by this function.