A car rental agency rents 200 cars per day at a rate of 29 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? R

Answer and Explanation:

Given:

Total car = 200

Rate = $29

Computation:

Total increase in rate = a

So, Total decrees in car = 5a

Total income (y) = [200-5a][29+a]

y = 5,800 + 200a - 145a - 5a²

y = 5,800 + 55a - 5a²

y' = dy / da [5,800 + 55a - 5a²]

y' = - 10a + 55

in which, y' = 0

0 = - 10a + 55

a = 5.5

So, Maximum rate = $ [29+5.5]

Maximum rate = $34.5

maximum income = 5,800 + 55 (5.5) - 5 (5.5) ²

maximum income = 5,800 + 302.5 - 151.25

maximum income = $5951.25