Answer to Question #257606 in Quantitative Methods for Bros

Question

An apartment complex has 250 apartments to rent. If they rent xx apartments then their monthly profit, in dollars, is given by,P(x)=−8x2+3200x−80,000P(x)=−8x2+3200x−80,000

How many apartments should they rent in order to maximize their profit?

Answer 1

$P'(x)=-16x+3200=0$

$x=3200/16=200$

$P(250)=220000$

$P(200)=240000$

$P(200)>P(250)$

So, it should be rented 200 apartments in order to maximize their profit.