Question

A car rental agency rents 220 cars per day at a rate of 28 dollars per day. For each 1 dollar increase in the daily rate, 6 fewer cars are rented. At what rate should the cars be rented to produce the maximum revenue, and what is the maximum revenue

Answer 1

The cars should be rented at $34 per day for a maximum income of $6268 per day.

If the daily rental is increased by $x

Then

Rental: R(x)=(28+x)dollars per car-day

Number of cars rented:  

N(x) = (220−6x) and Income: I(x) = (28+x) (220−6x) = 6,610 + 52x−5$x^{2}$ dollars/day.

The maximum will be achieved when the derivative of I (x) is zero.

$\frac{dI(x)}{dx}$ = 52−10x = 0

⇒ x = 5.2

For an even dollar rental amount, and increase of $5/day or $6/day will generate the same income.

So

$28+$5 = $33/day

or

$28+$6 = $34/day

would both be valid answers.

However, $34/day involves renting fewer cars and thus reduced expenses.

Using basic substitution and arithmetic

I(4) = $6,268

What is Maximum revenue ?

Maximum revenue is defined as the total maximum amount of revenue of product or service can yield at maximum demand and price.

To calculate maximum revenue, determine the revenue function and then find its maximum value. Write a formula where p equals price and q equals demand, in the number of units.

Learn more about Maximum revenue  on:

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