# optimzation problem # 22

• Aug 13th 2009, 09:34 AM
skeske1234
optimzation problem # 22
The manager of a 120 unit apartment complex knows from experience that all units will be occupied if the rent is 400 dollars a month. A market survey suggests that, on the average, one additional unit will remain vacant for each 10 dollar increase in rent. What rent should she charge to maximize revenue?

so this is what I have thus far:

I said that let x rep the number of dollar increases

(400+10x)

and so
120- (10x+400)
can be said to rep demand

Revenue will be
R=120-(10x+400) 10(x+400)

Question: do I have everything right so far? if i do, can I now proceed to find the maximum revenue or derivative of R
• Aug 13th 2009, 10:55 AM
skeeter
Quote:

Originally Posted by skeske1234
The manager of a 120 unit apartment complex knows from experience that all units will be occupied if the rent is 400 dollars a month. A market survey suggests that, on the average, one additional unit will remain vacant for each 10 dollar increase in rent. What rent should she charge to maximize revenue?

so this is what I have thus far:

I said that let x rep the number of dollar increases

(400+10x)

and so
120- (10x+400)
can be said to rep demand

Revenue will be
R=120-(10x+400) 10(x+400)

Question: do I have everything right so far? if i do, can I now proceed to find the maximum revenue or derivative of R

number of units occupied is (120-x)

revenue, R = (120-x)(400+10x)

note that when x is 0 (no price increase) , R = (120)(400)

when x = 1 price increase, one less unit is rented and R = (119)(410)

and so on ...

that's how to check the validity of the equation set up.