Acar rental agency has 150 cars. the owner finds that at a price of $48 per day, he can rent all the cars. for each $2 increase in price, the demand is less and 4 fewer cars are rented. for each car that is rented, there are routine maintenance costs of $5 per day. what rental charge will maximize profit?

Given that for each $2 increase in price, the demand is less and 4 fewer cars are rented.

Let x be the number of $2 increases in price, then the revenue from renting cars is given by
.

Also, given that for each car that is rented, there are routine maintenance costs of $5 per day, then the total cost of renting cars is given by


Profit is given by revenue - cost.
Thus, the profit from renting cars is given by


For maximum profit, the differentiation of the profit function equals zero.
i.e.


The price of renting a car is given by 48 + 2x = 48 + 2(8) = 48 + 16 = 64.

Therefore, the rental charge will maximize profit is $64.