If the cost function and revenue function of x units of an item are given by $C(x)=25x^2-x$ and $R(x)=4x$. Then the number of items to be produced to have maximum profit is,

$\frac{1}{10}$

The correct answer is Option (1) → $\frac{1}{10}$

The profit function P(x) is,

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

$=4x-(25x^2-x)$

$=-25x^2+5x$

for max. profit, $P'(c)=0$

$⇒-50c+5=0$

$⇒c=\frac{1}{10}$