Posted by JEUCD 12/1/11 on .
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?
You don't have to write the date its says it for you.
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