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

Answer:

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

Step-by-step 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,

⇒  $\frac{\partial \pi^A}{\partial f}$ = $20-2f =0$

                      $20=2f$  

                       $f=\frac{20}{2}$

                       $f=10$

On putting the value of "f", we get

⇒  $\pi^h=28h-h^2-10h$

         $=18h-h^2$

⇒  $\frac{\partial \pi h}{\partial h}=18-2h=0$

                      $2h=18$

                        $h=\frac{18}{2}$

                        $h=9$

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