# Calculus

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A car rental agency rents 180 cars per day at a rate of 32 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?

• Calculus -

You don't have to write the date its says it for you.

• Calculus -

let the number of \$1 increases be n
Number of cars sold = 180-5n
rate per car = 32+n
income = (32+n)(180-5n)
= 5760 + 20n -5n^2
d(income)/dn = 20 - 10n
= 0 for a max/min of income
10n = 20
n = 2

There should be two \$1 increases
they should be rented at \$34 and they should rent 170 cars for an income of 170(34) or \$5780

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