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 increase in rent. What rent should the manager charge to maximize revenue?

this is my work so far:
So i want maximize the revenue so I need an expression for the revenue.

revenue = (number of units rented) (rent per unit)

100 * $400 = $40 000

let increments be x:

The number of units rented would then be 100 - x and the rent per unit would be $400 + $5x. Hence the revenue would be

(100 - x)($400 + $5x)

Then i took the derivative of that function above to maximize it and i got x=30.

then i plugged in 30 in the revenue function and i got 4900 dollars. i don't think that right because increasing the rent from 800 to 4900 is too much.

would equation would i substitute x=30 in then?

  1. 👍 0
  2. 👎 0
  3. 👁 506
  1. I'm sorry -- but I don't know how to figure this out algebraically -- but I made a chart showing the revenue for rents up to $450. With 90 apartments occupied, the monthly revenue is $40,500. At this point the revenue keeps increasing. However, at rents of $500 and 80 units occupied, the total revenue is back at $40,000.

    1. 👍 0
    2. 👎 0
    👩‍🏫
    Ms. Sue
  2. as my total rent, i got 850 dollars.

    the man will increase the rent by a maxium of 50 dollars.

    i plugged in 30 into the revenue function and i got 4900.

    4900/100 is 49 dollars per unit.

    i rounded 49 to 50.

    1. 👍 0
    2. 👎 0
  3. I think you mean that the highest rent would be $450 per unit (not $850).

    I think there's something wrong with your numbers. However, you've found the right answer. The maximum rent should be $450 for 90 occupied apartments -- bringing in $40,500 a month to the apartment complex.

    1. 👍 0
    2. 👎 0
    👩‍🏫
    Ms. Sue
  4. You have the right values at x=30 but you have to multiple 30 times 5 which is 150 added to the original rent making the maximum revenue coming when you have 30 vacant rooms and have 70 rooms occupied
    Hope this helps

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting out x apartments is given by the following function. p(x)=-10x^2+1700x-43,000 To maximize the monthly rental

  2. Business

    Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation. Thomas’s fastest moving inventory item has a demand of 6000 units per year. The cost of each

  3. 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

  4. 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

  1. Math Please Help!!

    Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting x apartments is represented by the following function. P(x) = -8x2 + 1760x - 31000 (a) What is the actual profit

  2. Accounting

    If fixed costs are $250,000, the unit selling price is $125, and the unit variable costs are $73, what is the break-even sales (units)? Answer 3,425 units 2,381 units 2,000 units 4,808 units

  3. Calculus

    The manager of a large apartment complex knows from experience that 80 units will be occupied if the rent is 460 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 10

  4. Math

    3. A processor makes two components, A and B, which are then packaged together as the final product (each product sold contains one A and one B). The processor can do only one component at a time: either it can make As or it can

  1. physical

    Find the magnitude of the resultant of the following two vectors: i) 50 units due east and ii) 100 units 30° north of west. the answer is 62 unit but how it come ?

  2. MATH

    The quantity demanded for a certain brand of portable CD players is 200 units when the unit price is set at $90. The quantity demanded is 1,200 units when the unit price is $40. Find the demand equation. I'm leaning toward d, but

  3. Precalculus

    Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting out x apartments is given by the following function. P(x) = -10 x^2 + 1780 x - 54,000 To maximize the monthly

  4. Math

    Could someone work this question out so I understand it. Thanks The marginal price dp/dx at x units of demand per week is proportional to the price p. There is no weekly demand at a price of $100 per unit [p(0)=100], and there is

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