Calculus/Optimisation

A real estate manages 80 apartment units. When the rent of each unit is $180 per month, all units are occupied. However, for each $6 increase in rent, one of the units becomes vacant. Each occupied unit requires an average of $18 per month for service and repairs. What rent should be charged to realize the most profit?

  1. 👍 0
  2. 👎 0
  3. 👁 92
asked by Monica
  1. number of $6 increases ---- n

    right now:
    number rented = 80
    rent = 180

    after increase:
    rent = 180+6n
    number rented = 80-n

    revenue = (180+6n)(80-n) - 18(80-n)
    =14400 + 300n - 6n^2 - 1440 + 18n
    = -6n^2 + 318n + 12960
    = -6(n^2 - 53n - 2160)

    d(revenue)/dn = -6(2n - 53) = 0 for a max of revenue
    n = 53/2

    .....was expecting a whole number, check if typed correctly.

    1. 👍 0
    2. 👎 0
    posted by Reiny
  2. Yes the question is typed correctly but thank you!

    1. 👍 0
    2. 👎 0
    posted by Monica

Respond to this Question

First Name

Your Response

Similar Questions

  1. optimization calculus

    a real estate office manages 50 apartments in downtown building . when the rent is 900$ per month, all the units are occupied. for every 25$ increase in rent, one unit becomes vacant. on average , all units require 75$ in

    asked by Anonymous on March 10, 2011
  2. Calculus

    A real estate office manages 50 apartments in a downtown building. When the rent is $900 per month, all the units are occupied. For every $25 increase in rent, one unit becomes vacant. On average, all units require $75 in

    asked by Deepa on April 24, 2014
  3. Computer Programming

    I'm trying to create a vba code that solves this problem: 50 apartment units rent for 600 a month, for each 40 dollar increase in rent a unit becomes unoccupied. I want to find the max profit and number of units at that number.

    asked by Dom on July 9, 2013
  4. Calculus-Applied Optimization Problem

    The manager of a large apartment complex knows from experience that 100 units will be occupied if the rent is 425 dollars per month. A market survey suggests that, on average, one additional unit will remain vacant for each 9

    asked by Liz on October 31, 2013
  5. Math

    You are the manager of an apartment complex with 50 units. When you set rent at $800/month, all apartments are rented. As you increase rent by $25/month, one fewer apartment is rented. Maintenance costs run $50/month for each

    asked by Meghan on April 7, 2018
  6. Statistics

    The mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2,636. Assume the standard deviation is $500. A real estate firm samples 100 apartments. What is the probability that the average rent of the

    asked by Anonymous on June 20, 2013
  7. Calculus

    The manager of a 100 unit apartment complex knows from experience that all units will be occupied if the rent is $500 per month. A market survey suggests that, on average, one additional unit will remain vacant for each $10

    asked by Peter on March 2, 2010
  8. Math 1200

    a complex has 205 apartment units. When the rent is $635 per month all 205 units are occupied.Assume that for each $75 increase in rent 15 units becomes vacent. Assume that the number of occupied units is a linear function of the

    asked by Andrew on April 5, 2012
  9. please chech my answer optimization

    The manager of a 100-unit apartment complex knows from experience that all units will be occupied if the rent is $400 per month. A market survey suggests that, on the average, one additional unit will remain vacant for each $5

    asked by julie on November 11, 2007
  10. Statistics

    The mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2,651. Assume the standard deviation is $500. A real estate firm samples 100 apartments. What is the probability that the average rent of the

    asked by Tommy on October 6, 2015

More Similar Questions