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Name: The manager of a large apartment complex knows from experience that 90
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Description: The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 344 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 4 dollar increase in re

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 344 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 4 dollar increase in rent. Similarly, one additional unit will be occupied for each 4 dollar decrease in rent. What rent should the manager charge to maximize revenue?

Expert Solution

Step 1

let R be the revenue, and let n be the number of (up or down) $4 in rent.

Hence the equation for Revenue of increase of rent becomes:

$R = (90 - n) (344 + 4 n) R = 30960 - 344 n + 360 n - 4 n^{2} R = - 4 n^{2} + 16 n + 30960$

Now for rent increase,

$n_{m a x} = - 8 n + 16 = 0 8 n = 16 n = 2$

Hence,

$R = (90 - 2) (344 + 8) = 30, 976$

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