# Max revenue problem

1. Nov 18, 2006

### Alain12345

I have a problem that I need help with. I tried to solve it, but I don't know how. I don't have much trouble solving simpler min and max problems, but when they start throwing in more numbers, I get confused.

The landlord of a 40-unit apartment building is planning to increase the rent. Currently residents pay $700/month. Four units are vacant. A real estate agency has found that, in this market, every$25 increase in monthly rent results in one more vacant unit. What rent should the landlord charge to maximize revenue?

I know I have to come up with something and get the derivative of that then find the critical number, but if I can't get the first part, I can't continue to solve the problem...

Thanks

2. Nov 18, 2006

### buzzmath

he is currently renting 36 units at $700 so he makes 36*700 dollars a month. An increase of$25 a month would give 725*35 dollars a month and so on. So if x is the number of \$25 dollar increases a month then
(700+x25) is the amount he charges his residents each month and (36-x) is the number of residents he will have. Can you come up with a function to tell how much money he'll make a month with this information? Once you have this maximize it