Question

the manager of an apartment complex knows that 110 units will be occupied if rent is $324/month. On average, one additional unit will remain vacant for each $1 increase in rent. Similarly, one additional unit will be occupied for each $1 decrease in rent. What rent should the manager charge to maximize revenue?

Answer 1

Unless typos, all the 110 units will be occupied at $324 per month. Since the manager has full occupancy, I see no reason to change.

Answer 2

suppose there have been x $1 increases.
Since revenue = price * quantity,
r(x) = (324+x)(110-x)
The vertex (maximum revenue) is at (-107,47089)
So he should charge 324-107 = $217 rent, assuming he has 110+107 = 217 units available.