Lynbrook West , an apartment has 100 two-bedroom units. The montly profit realized from renting out x apartments is given by the following function

Bergen 2021-09-08 Answered
Lynbrook West , an apartment complex , has 100 two-bedroom units. The montly profit (in dollars) realized from renting out x apartments is given by the following function.
P(x)=12x2+2136x41000
To maximize the monthly rental profit , how many units should be rented out?
What is the maximum monthly profit realizable?
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Expert Answer

SoosteethicU
Answered 2021-09-09 Author has 102 answers

Step 1
Given profit function ,
P(x)=12x2+2136x41000
To maximize profit
ddxP(x)=0
ddx(12x2+2136x41000)=0
24x+2136=0
24x=2136
x=213624
x=89
Here , d2P(x)dx2=24<0
as per second derirative test profit is maximum at x=89
Also , maximum profit
=P(89)=12(89)2+2136(89)41000
=54052
To maximize the montly rental profit, 89 units should be rented out, 54052$ be the maximum monthly profit

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