Question

A car rental agency rents 180 cars per day at a rate of 32 dollars per day. For each 1 dollar increase in the daily rate, 5 fewer cars are rented. At what rate should the cars be rented to produce the maximum income, and what is the maximum income?

Answer 1

You don't have to write the date its says it for you.

Answer 2

let the number of $1 increases be n
Number of cars sold = 180-5n
rate per car = 32+n
income = (32+n)(180-5n)
= 5760 + 20n -5n^2
d(income)/dn = 20 - 10n
= 0 for a max/min of income
10n = 20
n = 2

There should be two $1 increases
they should be rented at $34 and they should rent 170 cars for an income of 170(34) or $5780