# A car rental agency rents 220 cars per day at a rate of 27 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?

##### 1 Answer

Jul 9, 2015

Assuming an even dollar rental is required;

The cars should be rented at $36 per day for a maximum income of $6300 per day.

#### Explanation:

If the daily rental is increased by $

then

Rental:

Number of cars rented:

and

Income:

The maximum will be achieved when the derivative of

For an even dollar rental amount, and increase of $8/day or $9/day will generate the same income.

So

or

would both be valid answers.

However, $36/day involves renting fewer cars and thus reduced expenses.

Using basic substitution and arithmetic