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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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