A car rental agency rents 180 cars per day at a rate of 27 dollars per day.

Question

A car rental agency rents 180 cars per day at a rate of 27 dollars per day. For each 1 dollar increase in the daily rate, 5 fewer cars are rented. At what rate should the cars be rented to produce the maximum income, and what is the maximum income? 

Answer 1

f(x) = (27 + x) * (180 - 5x)

f ' (x) = 1 * (180 - 5x) + (27 + x) * (-5) = =

= 180 - 5x -135 - 5x = 0

= -10x + 45 = 0

= -10 x = -45

x = 4.5