The price p per unit if an article is p = 75 - 2x and the cost function is given by $C(x)= 250 + 10x+\frac{x^2}{2}$

For, maximum profit, the number of units sold are :

13

The correct answer is Option (1) → 13

Revenue is calculated as,

$R(x)=x.p=x(75-2x)$

$=75x-2x^2$

Cost function, $C(x)=250+10x+\frac{x^2}{2}$

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

$=75x-2x^2-250-10x-\frac{x^2}{2}$

$=-250+65x-\frac{5x^2}{2}$

To find critical points,

$f'(c)=0$

$⇒65-5x=0$

$⇒x=\frac{65}{5}=13\,units$