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 :
Answer & explanation
Correct answer: option 1
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,
$f'(c)=0$
$⇒65-5x=0$
$⇒x=\frac{65}{5}=13\,units$