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

I don't even know the answer to this one. I don't understand at all, please help me step by step

  1. 👍
  2. 👎
  3. 👁
  1. right now:
    price of rent = 900
    number of units rented = 50

    Let the number of $25 increases be n
    (e.g. If n= 2 , new rent is 900+2(25) = 950
    if n = 5 , the new rent 900 + 5(25) = 1025

    so the new rent = 900 + 25n
    number rented = 50-n
    maintenance cost = 75(50-n)

    Profit = P = (900+25n)(50-n) - 75(50-n)
    = 45000 + 350n - 25n^2 - 3750 + 75n
    = 41250 + 425n - 25n^2

    d(profit)/dn = 425 - 50n
    = 0 for a max of P
    50n = 425
    n = 8.5

    The question did not say if increases are in whole multiples of 25 , but I will assume that. We could not rent 50-8.5 or 41.5 units.

    when n = 8 or n = 9

    if n = 8
    number rented = 42
    rent = 900+8(25) = 1100
    maintenace cost = 75(42) = 3150
    Profit = 42x1100 - 3150 = 43050

    if n = 9
    number rented = 41
    rent = 1125
    maintenance cost = 3075
    Profit = 41x1125 - 3075 = 43050 , as expected.

    1. 👍
    2. 👎
  2. Wow thankyou sooooo much! you saved me xD

    1. 👍
    2. 👎
  3. I'm interested in multi-unit buildings from 8 214 maybe just 20 apartment buildings if you do call me please leave me a voicemail because I'm a professional boxer and people call me from all around the world and you could send me a link awesome to my email. Luis_mateo12. my cell number 773 680 5343 please leave me a voicemail and let me know as you and I will definitely call you back because a lot of people just call me for nonsense

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. language

    Vote No on the Highway 85 Extension by Victoria Vail, Tribune staff writer Next week, the city council will consider a proposal to extend Highway 85 by 10 miles. A small coalition of real estate developers have hurried this

  2. 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

  3. Calculus

    Let r be the monthly rent per unit in an apartment building with 100 units. All the units are rented at r= $900. One unit becomes vacant for each $10 increase in rent. Maintenance cost are $100 for occupied units and nothing for

  4. statistics

    David wants to rent an unfurnished apartment for next semester. He took a random sample of 9 apartments adversised in the local Halifax paper, and recorded the rental rates. The rents (in $ per month) were: 500 650 600 505 450 550

  1. Math

    A real estate company owns 218 efficiency apartments, which are fully occupied when the rent is $940 /month. The company estimated that for each $25 increase in rent, 5 apartments will become unoccupied. What rent should be

  2. ELA

    Analyze Informational Text Unit Test Use the article to complete the activity. Vote No on the Highway 85 Extension by Victoria Vail, Tribune staff writer Next week, the city council will consider a proposal to extend Highway 85 by

  3. (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

  4. 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

  1. Programming Logic and Design

    Mr. Roper owns 20 apartment buildings. Each building contains 15 units that he rents for $800 per month each. Design the application that would print 12 payment coupons for each of the 15 apartments in each of the 20 buildings.

  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. 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?

  4. 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

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