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Max revenue problem

  1. Nov 18, 2006 #1
    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. jcsd
  3. Nov 18, 2006 #2
    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
     
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