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 :

50

The correct answer is Option (3) → 50

The Demand function is,

$p=20+2x-\frac{x^2}{30}$

$R(x)=x.p=x\left(20+2x-\frac{x^2}{30}\right)$

$=20x+2x^2-\frac{x^3}{30}$

$MR(x)=\frac{d}{dx}\left(20+2x^2-\frac{x^3}{30}\right)$

$=20+4x-\frac{3x^2}{30}$

$⇒MR(10)=20+4(10)-\frac{3×(10)^2}{30}=50$