Posted by **JEUCD 12/1/11** on Thursday, December 1, 2011 at 5:30pm.

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?

- Calculus -
**Laruen **, Thursday, December 1, 2011 at 5:41pm
You don't have to write the date its says it for you.

- Calculus -
**Reiny**, Thursday, December 1, 2011 at 5:46pm
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

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