Question

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

Answer 1

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".