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