The demand for a certain product is represented by the function $p=20+2x-\frac{x^2}{30}$ where c is the number of units demanded and p is the price per unit , then the value of marginal revenue when 10 units are sold is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 50
The Demand function is,
$p=20+2x-\frac{x^2}{30}$
$R(x)=x.p=x\left(20+2x-\frac{x^2}{30}\right)$
$=20x+2x^2-\frac{x^3}{30}$
$MR(x)=\frac{d}{dx}\left(20+2x^2-\frac{x^3}{30}\right)$
$=20+4x-\frac{3x^2}{30}$
$⇒MR(10)=20+4(10)-\frac{3×(10)^2}{30}=50$