# 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.

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• Anonymous
2 months ago

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.

• Edna
Lv 7
2 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.

• Anonymous
2 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.

• Erik
Lv 7
2 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.

• Anonymous
2 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..

• Erik
Lv 7
2 months agoReport

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

• 2 months ago

Do your own damn homework.

• Erik
Lv 7
2 months ago

I did it the somewhat long way (not every number) and got \$99 per car.