Answer to Question #3656 in Calculus for joe

Question

A real estate firm owns 100 garden type apartments at $400/month. For each $10/ month increase there will be two vacancies with no possibility of filling them. What rent per month will max monthly revenue?

Answer 1

R is a revenue. If the price is (400+10n) then there will be (100-2n) apartments rented.
R =(100-2n)(400+10n) → max
R' =(40000+200n-20n² )' = 200 - 40n
R' =0 => n=5
R'' = -40 => n=5 - point of maximum
(100-2*5)(400+10*5)=40500
So, max revenue is $40,500 with the price $450/month.