Question

A car rental agency has 24 cars (each an identical model). The owner of the agency finds that at a price of $18 per day, all the cars can be rented; however, for each $1 increase in rental cost, one of the cars is not rented. What should the agency charge to maximize income?

Answer 1

To maximize income, the car rental agency should charge $41 per day.

Step-by-step explanation:

To maximize income, the car rental agency should charge a price at which all 24 cars can be rented out. We know that at a price of $18 per day, all the cars can be rented. However, for each $1 increase in rental cost, one car is not rented. So, if the agency charges $19 per day, 23 cars will be rented. The agency should continue increasing the price until only one car remains unrented. This happens when the agency charges $18 + (24 - 1) = $41 per day. At this price, the agency will maximize its income.