Calculus

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?

  1. 👍
  2. 👎
  3. 👁
  1. You don't have to write the date its says it for you.

    1. 👍
    2. 👎
  2. 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

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. algebra

    Ace car rental rents a car for $45 and .25 cents per mile. Star rental car rents a car for $35 and .30 cents per mile. How many miles would a driver need to drive before the cost of renting a car at these two places were the same?

  2. Survey of Mathematics

    Suppose a car rental agency gives the following choices: Option A: $30 per day plus 40 cents per mile Option B: flat $50 per day (unlimited miles) At what mileage are both rates the same if you rent the car for 3 days?

  3. Math, I NEED HELP.c:

    A rental company charges a flat fee of x dollars for a floor sander rental plus y dollars per hour of the rental. One customer rents a floor sander for 4 hours and pays $63. Another customer rents a floor sander for 6 hours and

  4. math

    please help me check!! James rents a car for x days. the rate is 19.95 per day, which includes 20 miles of driving and .40 per mile for each additional mile. If James drives 30 miles per day for the duration of this period, which

  1. math

    A car-rental agency charges $38 per day plus $0.21 for each mile driven. Sandra paid $88.40 for renting a car from them for one day. Write an equation to find the number of miles she drove that day.

  2. Math

    A rental car agency charges $15 per day plus $.11 per mile to rent a certain car. Another agency charges $18 per day plus 8 cents per mile to rent the same car. If they rent the car for one day how many miles will they have to be

  3. Algebra

    A car rental agency advertised renting a car for $24.95 per day and $0.33 per mile.If David rents this car for 3 days, how many whole miles can he drive on a $100 budget?

  4. Algebra 2

    Janine is considering two movie rental plans. Plan A can be modeled with the equation C=3m and Plan B can be modeled with the equation C=2m+5 where C represents the cost in dollars and M represents the number of movies rented each

  1. Statistics

    A car rental agency currently has 41 cars available, 28 of which have a GPS navigation system. Two cars are selected at random from these 41 cars. Find the probability that both of these cars have GPS navigation systems

  2. Problem solving

    A rental car agency charges $15 per day plus $.11 per mile to rent a certain car. Another agency charges $18 per day plus 8 cents per mile to rent the same car. If they rent the car for one day how many miles will they have to be

  3. Math

    The cost of renting a car is given by the formula C= 50n +0.15d, where C is the cost in dollars, n is the number of days rental, and d is the distance driven in miles. How much would it cost to rent a car for a 15- day road trip,

  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

You can view more similar questions or ask a new question.