Question

The manager of a large apartment complex knows from experience that 110 units will be occupied if the rent is 324 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 9 dollar increase in rent. Similarly, one additional unit will be occupied for each 9 dollar decrease in rent. What rent should the manager charge to maximize revenue?

This is an optimization problem and I have a really hard time doing these so if someone could help it would be great! Thank you! :)

Answer 1

\[R = revenue\]
\[R = (110-x)(324+9x) \ge 0\ \\x \epsilon (0, 110)\]
\[R' = -18(x-37)\]
Now test:
When R'=0, x=37
When R'=DNE, it's impossible

Now using second derivative test to check if x=37 is a local max or local min:
\[R''=-18\] This is a negative number, which means it's a local max.

Hence, rent is \[342+9x=342+9\times18=504$\]

Answer 2

No :(

Answer 3

Try 657

Answer 4

yup works

Answer 5

Thank you :) can you look at my other question I posted and I'll post my last one right now if you don't mind helping me with those :)

Answer 6

Alright