The maximum revenue for all the demand function $P(x)=\frac{80-x}{4}$ is equal to:

400

The correct answer is Option (2) → 400

The Revenue function is,

$R(x)=x.P(x)$

$=x\left(\frac{80-x}{4}\right)=\frac{80x-x^2}{4}$

$R'(x)=\frac{80-2x}{4}$

for critical points, $R'(c)=0$

$⇒\frac{80-2c}{4}=0$

$⇒c=40$

$R(40)=\frac{80×40-40×40}{4}=\frac{40×40}{4}=400$