A Television manufacturing company can sell x television per month at  $₹\left(40-\frac{x}{2}\right)$ each. The cost of production of x television per month is $₹\frac{x^2}{2}$.  The maximum profit of the company per month is :

₹400

The correct answer is Option (1) → ₹400

The revenue $R(x)$ is,

$R(x)=x\left(40-\frac{x}{2}\right)=40x-\frac{x^2}{2}$

$P(x)=R(x)-C(x)$

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

$=40x-x^2$

$\frac{d(P(x))}{dx}=40-2x=0$

$x=20$

$P(20)=(40×20)-(20)^2$

$=800-400$

$=400$