# A car rental company has 426 cars on their lot. They can rent all 426 cars at a rate of $56 per day. ?

They determine that for every $1 increase in the rental cost, they will rent 3 fewer cars. Find the car rental rate that will maximize revenue for the company.

### 7 Answers

- Anonymous2 months agoFavorite Answer
Revenue = Rental rate times the number of cars rented out

If you let x the rate increase, and R is the revenue

Rental rate = $56 + $1(x)

Number of cars rented out = 426-3x

R as a function of x = (56 + x)(426-3x)

Simplify the equation and then get the derivative of the function. Get the derivative to equal zero, then solve for x.

Your answer should be x = 43

Rental rate = $99 and 297 cars will be rented out.

Oooops, edited after review.

- Login to reply the answers

- EdnaLv 72 months ago
I'm not going to try to figure out the car rental rate for you, because no car rental company has 426 cars on their lot at one time. Not even new car dealerships have that many cars on their lot.

- Login to reply the answers

- Anonymous2 months ago
If they lose 3 rentals a day at $57, then why increase the fee. They're already renting all 426 @ $56. That's the maximum.

- ErikLv 72 months agoReport
Because if they can get an extra dollar, that's $423 more. And they only lose $171 due to not renting the three cars.

- Login to reply the answers

- Anonymous2 months ago
I don't know not do I car. not do they only make money from renting the car. you bring it back without enough gas they will charge you for that and believe me they will charge you plenty. Insurance, taxes other fees. Believe me they make money and plenty of it..

It's obvious that this is a math problem. No car rental place rents the same number of cars every day.

- Login to reply the answers

- How do you think about the answers? You can sign in to vote the answer.
- ErikLv 72 months ago
I did it the somewhat long way (not every number) and got $99 per car.

- Login to reply the answers

- Anonymous2 months ago
Calculate how much they will make if they rent out 425 cars. Then do it for 424 cars and so on until the total starts to drop from the last number. voila.

- Login to reply the answers