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:
⇒ [tex]\pi^h=28h-h^2-hf[/tex]
If airport won't pay any cost for the damage,
⇒ [tex]\pi^A=20f-f^2[/tex]
then,
⇒ [tex]\frac{\partial \pi^A}{\partial f}[/tex] = [tex]20-2f =0[/tex]
[tex]20=2f[/tex]
[tex]f=\frac{20}{2}[/tex]
[tex]f=10[/tex]
On putting the value of "f", we get
⇒ [tex]\pi^h=28h-h^2-10h[/tex]
[tex]=18h-h^2[/tex]
⇒ [tex]\frac{\partial \pi h}{\partial h}=18-2h=0[/tex]
[tex]2h=18[/tex]
[tex]h=\frac{18}{2}[/tex]
[tex]h=9[/tex]
So that the total number of house built by the developers will be "9".
