Calculus

posted by .

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

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. AP Calculus AB

    A traffic engineer monitors the rate at which cars enter a freeway onramp during rush hour. From her data, she estimates that between 4:30 pm and 5:30 pm, the rate R(t) at which cars enter is given by: R(t)=100(1-0.00012t^2) cars per …
  2. Probability

    rent-4-wheels makes a profit of $12 per day for each car rented, and loses $4 per day for each car that is not rented. How many cars should the company have on hand to maximize profit, subject to the following probability distribution: …
  3. math

    ent-4-wheels makes a profit of $12 per day for each car rented, and loses $4 per day for each car that is not rented. How many cars should the company have on hand to maximize profit, subject to the following probability distribution: …
  4. programming

    This pseudocode should detrmine the rental fees for cars // Standard cars rent for $65 per day; compacts rent for $40 per day // and subcompacts rent for $30 per day // Rentals for at least 7 days receive a 20% discount // An error …
  5. FInite Math

    A car rental agency has rental and return facilities at both Dallas and Austin Airports. Assume that a car rented at either airport must be returned to one or the other airport. If a car is rented at Austin, the probability that it …
  6. math

    Bay Area Rental Cars charges $18 a day and $.14 per mile for renting a car. You rented a car for 4 days and drove 313 miles. Find your total cost for renting the car.
  7. Computer programming

    I am trying to write a program in C that would be used by a car rental company. This program finds the subtotal, tax amount(6%) and finally the total. The user enters in how many days the car was rented and how many miles were driven. …
  8. Algebra

    a car rental company has two rates. The first rate is 45$ per day plus 29.5 cents per mile the second rare is 90$ per day plus 0.07 per mile. If you rented at the 90$ rate, how many miles you would need to drive to break even?
  9. computer science

    Acarrentalcompanyusesthefollowingtabletohelpcomputerentalfees. TABLE 9.3 Car Type Chevrolet Corvette Pontiac Buick Oldsmobile Cadillac Rate per Day 50.00 85.00 53.00 60.00 60.00 70.00 Rate per Mile 0.27 0.45 0.32 0.32 0.35 0.40 Write …
  10. computer science

    Acarrentalcompanyusesthefollowingtabletohelpcomputerentalfees. TABLE 9.3 Car Type Chevrolet Corvette Pontiac Buick Oldsmobile Cadillac Rate per Day 50.00 85.00 53.00 60.00 60.00 70.00 Rate per Mile 0.27 0.45 0.32 0.32 0.35 0.40 Write …

More Similar Questions