How much does a 100 unit apartment complex cost

Asked by maham237 @ in Mathematics viewed by 300 People

All units of a 100 unit apartment complex are rented out when the monthly rent is set at$1000 per month. suppose that one unit becomes empty with each $10 increase in rent and that each occupied unit costs $200 per month in maintenance.what is the amount of rent per month that will maximize monthly profit?
a.) what is the equation we are trying to optimize? what is the domain?
b.)1.)what is the optimal number of apartments to rent?
2.)what is the optimal monthly rent per unit?
3.)what is the maximum profit?
--------------------------------------------------
is the attached photo right if not please explain why
--------------------------------------------------

Answered by maham237 @


Your picture has several issues.

  1. x is not defined. It appears to be the number of apartments rented.
  2. R(x) is defined two different ways. The first way, it looks like it is the revenue from a single apartment. The second way, it looks like it is the revenue from the entire apartment complex.
  3. The derivative is in error. It should be -20x +2000. In any event, this is not the derivative you want. You're not trying to maximize revenue; you're trying to maximize profit.
  4. It might be useful to write an equation for profit: P(x) = R(x) -200x = -10x² +1800x. Then when you go to maximize it, your derivative will be P'(x) = 0 = -20x +1800 ⇒ x = 90.

Your answer is correct, but the path you followed to get there has a few potholes.


Similar Questions

If 100 envelopes cost 70 cents, how much would 250 cost?

Asked by maham237 @ in Mathematics viewed by 360 persons

How much does it cost per acre to plant corn

Asked by admin @ in Mathematics viewed by 345 persons

Seed costs for a farmer are $40 per acre for corn and $32 per acre for soybeans. How many acres of each crop should the farmer plant if he wants …

How much does it cost to rent a revel scooter

Asked by admin @ in Mathematics viewed by 350 persons

Revel and Scooters are the best scooter experience in the Nation which is the best scooter rental service in the nation? Create a graph to determine if the hours and …

How much does it cost to carpet a 10x12 room

Asked by admin @ in Mathematics viewed by 302 persons

ann is putting carpet in a room that is 12 feet long by 10 feet wide. the carpet costs $3.00 per square foot. How much will the carpet for the …

How much did it cost to build the brooklyn bridge

Asked by admin @ in History viewed by 303 persons

Ote that the Brooklyn Bridge, or Great East River Bridge, was the largest suspension bridge to be built at this time. How does the author recreate the excitement of the …

How much does a 6 pack of coca cola cost

Asked by admin @ in Mathematics viewed by 293 persons

A six-pack of soda cost 2.46. What is the cost of can of soda?

How much does a 80 pound bag of concrete cost

Asked by admin @ in Mathematics viewed by 360 persons

An 80-pound bag of concrete mix will yield 0.6 cubic feet of concrete. Each bag costs $4.98. An artist wants to make a concrete sculpture consisting of three cubes, one …

How much does a 4 pound package cost to ship

Asked by admin @ in Mathematics viewed by 313 persons

To package and ship an item, it cost $5.75 for the first pound and $0.75 for each additional pound. What is the cost of shipping a 12-pound package?

How much does it cost to rent out sky zone

Asked by admin @ in Mathematics viewed by 266 persons

To have a party at Sky Zone, it cost $125 to rent the room and $5.25 a person for pizza and drinks. The following equation represents the total amount to …

How much does it cost to buy a beagle puppy

Asked by admin @ in Mathematics viewed by 312 persons

The price of 6 week old Beagle puppies are $339.50 but they're coming on sale this Friday and will be 20% cheaper. How much will the puppy cost me if …

How much does it cost for a cell phone plan

Asked by admin @ in Mathematics viewed by 335 persons

7. Han's cell phone plan costs $200 to start. Then there is a $50 charge each month. a. What is the total cost (start up fee and monthly charge) to …

How much does it cost to run a concession stand

Asked by admin @ in Mathematics viewed by 302 persons

You are running a concession stand at a game. You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of …

How much does it cost to pour concrete per yard

Asked by admin @ in Mathematics viewed by 311 persons

Concrete can be purchased by the cubic yard. How much will it cost to pour a slab 18 feet by 18 feet by 4 inches for a patio if the …

Places a and b are 100 km apart

Asked by admin @ in Math viewed by 267 persons

Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the …

How much is 100 shares of stock

Asked by maham237 @ in Mathematics viewed by 486 persons

You bought 100 shares of stock at $15 per share. You sold your 100 shares at $21.75 per share. Calculate your percentage of gain.

Most viewed questions in Mathematics

Unit 6 similar triangles homework 2 similar figures answer key

Asked by maham237 @ in Mathematics viewed by 18324 persons

All things algebra unit 7 polygons and quadrilaterals answer key

Asked by admin @ in Mathematics viewed by 8115 persons

Gina wilson all things algebra 2016 answer key unit 11

Asked by admin @ in Mathematics viewed by 5752 persons

Unit 1 geometry basics homework 4 angle addition postulate answers

Asked by maham237 @ in Mathematics viewed by 3925 persons

Unit 6 exponents and exponential functions homework 8 answer key

Asked by maham237 @ in Mathematics viewed by 3240 persons

The manager of a vacation resort believes that the ages

Asked by maham237 @ in Mathematics viewed by 2912 persons

What is 271 403 rounded to the nearest ten thousand

Asked by maham237 @ in Mathematics viewed by 2777 persons

Unit 1 geometry basics homework 3 angle relationships answer key

Asked by maham237 @ in Mathematics viewed by 2567 persons

Homework 2 parallelograms

Asked by maham237 @ in Mathematics viewed by 2485 persons

Why would a prism beat a sphere in a competition?

Asked by maham237 @ in Mathematics viewed by 2472 persons

John wants to send a letter to peter

Asked by maham237 @ in Mathematics viewed by 2452 persons

An artist sells a painting for 20.50 but uses 5.75

Asked by maham237 @ in Mathematics viewed by 2419 persons

Unit 4 congruent triangles homework 1 classifying triangles answer key

Asked by maham237 @ in Mathematics viewed by 2412 persons

Unit 4 congruent triangles homework 2 angles of triangles

Asked by maham237 @ in Mathematics viewed by 2067 persons

Compare the values of the 2s and 5s in 55220

Asked by maham237 @ in Mathematics viewed by 1786 persons