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 :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → ₹400
The revenue $R(x)$ is,
$R(x)=x\left(40-\frac{x}{2}\right)=40x-\frac{x^2}{2}$
$P(x)=R(x)-C(x)$
$=\left(4x-\frac{x^2}{2}\right)-\frac{x^2}{2}$
$=40x-x^2$
$\frac{d(P(x))}{dx}=40-2x=0$
$x=20$
$P(20)=(40×20)-(20)^2$
$=800-400$
$=400$