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 maintenance and repairs each month. how much rent should be real estate office charge to maximize profits?

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  1. let the number of $25 increases be n
    new rent = 900 + 25n
    number rented = 50-n

    profit = (50-n)(900+25n) - 75n
    = 45000+275n - 25n^2

    d(profit)/dn = 275 - 50n = 0 for max/min of profit
    50n = 275
    n = 275/50 = 5.5

    The question is not clear whether the increases have to be in exact jumps of $25.
    if so, then n=5 or n=6 will yield the same profit
    e.g.
    if n=6, profit = 45000+1650-900 = 45750
    if n=5 , profit = 45000+1375-625 = 45750

    if a partial increase is allowed, then
    n = 5.5
    new rent = 1037.50
    number rented = 50-5.5 = 44.5 ???? (makes no real sense)
    but mathematically profit
    = 45000+5.5(275)-25(5.5)^2 = 45756.25

    I would go with either n=5 or n=6

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Respond to this Question

First Name

Your Response

Similar Questions

  1. FP/101

    Which of the following is considered an advantage of home ownership? A. You are responsible for all repairs and maintenance. B. Interest paid on the mortgage of your home is tax deductible. C. Mortgage payments are always lower

  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

  3. 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

  4. algebra

    You rent an apartment that costs \$900$900 per month during the first year, but the rent is set to go up 7.5% per year. What would be the rent of the apartment during the 7th year of living in the apartment? Round to the nearest

  1. math

    The windows of a downtown office building are arranged so that each floor has six fewer windows than the floor below it. If the ground floor has 52 windows, how many total windows are on the first eight floors?

  2. Stats

    You want to rent an unfurnished one-bedroom apartment in Boston next year. The mean monthly rent for a random sample of 14 apartments advertised in the local newspaper is $1200. Assume that the standard deviation is $230. Find a

  3. Math

    Scott Mason purchased a 5-unit apartment building as an investment before he retired. From the rent he collects each month, Scott pays out $1,025 for expenses. How much rent must he charge for each of the 5 apartments if he wants

  4. MATH

    1. Which is equivalent to this expression? 9 – 5(4 – 2) / 3 + 5 A. -13/8 B. -1/8 C. 1 *** D. 7/4 2. There are 2 linen closets and 3 walk-in closets in each apartment in a building. The total number of closets in the building

  1. (basic)accounting help plz!

    June 1: Rented office space and paid three months’ rent in advance, $3,000, cheque 601. Ans: Rent expense (DEBIT) Cash (CREDIT) adjustment: a) One month’s rent had expired. i think it will be: prepaid rent (DEBIT $2000) rent

  2. Phisycs

    Lake Point Tower in Chicago is the tallest apartment building in the United States (although not the tallest building in which there are apartments).Suppose you take the elevator from street level to the roof of the building.The

  3. Operation

    Parsa Real Estate is a company that buys and rents real estate. The company is looking into buying an office building for $1M.Thebuilding has 10,000 square feet of rentable office space. The company analysts predict that they can

  4. stats

    Cushman and Wakefield accounting that the average annual rent for office space in Tampa was $17.63 per square foot. A real estate agent selected a random sample of 15 rental properties (offices) and found that mean rent was $18.72

View more similar questions or ask a new question.