The maximum revenue for all the demand function $P(x)=\frac{80-x}{4}$ is equal to:
Answer & explanation
Correct answer: option 2
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, $R'(c)=0$
$⇒\frac{80-2c}{4}=0$
$⇒c=40$
$R(40)=\frac{80×40-40×40}{4}=\frac{40×40}{4}=400$