A company is selling a certain product. The demand function of the product is linear. The company can sell 1000 units when the price is ₹8 per unit and when the price is ₹4 per unit, it can sell 2000 units. The total revenue function (R(x)) is given by :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{-x^2}{250}+12x$
$R(x)=p(x).x$
Since the demand function is linear
$p(x)=mx+c$
Here, m ⇒ slope, c ⇒ intercept
Points of demand function (given)
$x=1000,p=8$
$x=2000,p=4$
$M=\frac{p_2-p_1}{x_2-x_1}=\frac{4-8}{2000-1000}=\frac{-4}{1000}=\frac{-1}{250}$
$P(x)=\frac{-1}{250}x+c$
Using point (1000, 8)
$8=\frac{-1}{250}(1000)+c$
$8=-4+c$
$c=12$
$∴P(x)=\frac{-1}{250}x+12$
$R(x)=\left(\frac{-1}{250}x+12\right)x$
$=\frac{-1}{250}x^2+12x$