The manager of a large apartment complex knows from experience that 100 units wi
ID: 2837918 • Letter: T
Question
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 2 dollar increase in rent. Similarly, one additional unit will be occupied for each 2 dollar decrease in rent.
Let the rent on an apartment be x dollars per month, and let N be the number of apartments rented each month, and let R be the revenue (the gross income) brought in each month by the apartment manager.
(1 pt) Get help entering answers pi Note: You may use decimals n your answer for this problem The manager of a large apartment complex knows from experience that 100 units will be occupied if the rent is 125 dollars per month. A market survey suggests that, on average, one additional unit will remain vacant for each 2 dollar increase in rent. Similarly, one additional unit will be occupied for each 2 dollar decrease in rent. Let the rent on an apartment be x dollars per month, and let N be the number of apartments rented each month, and let R be the revenue (the gross income) brought in each month by the apartment manager. Write N as a function of x only. N(x) = apartments. Write R as a function of x only. R(x) = dollars. What rent should the manager charge to maximize revenue? ANSWER: Pi rs per month. Important: On an exam you will be expected to use the techniques of MTH 132 to justify that you have found the amount of rent which maximizes revenue. Note: You can earn partial credit on this problem.Explanation / Answer
I have solved this question earlier with different figures. Please workout using yours figures. If you need any further help just PM me. If I have helped you please rate me 5 stars first (before you rate anyone else)
The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 348 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 2 dollar increase in rent. Similarly, one additional unit will be occupied for each 2 dollar decrease in rent. What rent should the manager charge to maximize revenue?
Answer
Let R = rent in dollars
Number of occupied units = 90 + (348-R)/2 = 264 - R/2
Revenue = R(264 - R/2) = 264R - R^2/2
We have a quadratic equation in one variable, so it's going to be a parabola.
Revenue will be 0 when R=0 or R/2 = 264 (meaning R=528)
Maximum revenue will be halfway between those two, at R=264.
$264 per month is what he should be charging.
Yep. Anything higher or lower than that $264 rent will earn him less revenue.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.