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An airport is located next to a housing development. Profits to the airport are simply 20 f-f 2, where f is the number of flights per day. The housing developers profits are 28hh2-h, where h is the number of houses and f is the number of flights per day. If the airport is not required to pay the developer for any "damages" from the flights, how many houses will the developer build

1 Answer

4 votes

Answer:

The total number of houses are "9". The further explanation is given below.

Explanation:

The given values are:

height,

h = 28h - h²

Housing profit of developers will be:


\pi^h=28h-h^2-hf

If airport won't pay any cost for the damage,


\pi^A=20f-f^2

then,


(\partial \pi^A)/(\partial f) =
20-2f =0


20=2f


f=(20)/(2)


f=10

On putting the value of "f", we get


\pi^h=28h-h^2-10h


=18h-h^2


(\partial \pi h)/(\partial h)=18-2h=0


2h=18


h=(18)/(2)


h=9

So that the total number of house built by the developers will be "9".

User Tony Adams
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