A car rental company has 468 cars on their lot They can rent

A car rental company has 468 cars on their lot, They can rent all 468 cars at a rate of $30 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. Best rate: $

Solution

total number of cars = 468

rent = $ 30 per day

revenue function can be written as

R(x) = ( 30 + 1x) ( 468 - 3x)

R(x) = -3x^2+378x + 14040

maximum revenue occurs at x = -378 / 2(-3) = 63

and maximum revenue will be $ 25947