The total cost and revenue function of a commodity are given by $C(x)=x+40$ and $R(x)=10 x-0.2 x^2$. Then break even points are:

5, 40

The correct answer is Option (2) → 5, 40

$C(x) = x + 40,\;\; R(x) = 10x - 0.2x^2$

$\text{Break-even when } R(x) = C(x)$

$10x - 0.2x^2 = x + 40$

$-0.2x^2 + 9x - 40 = 0$

$x^2 - 45x + 200 = 0$

$x^2 - 45x + 200 = 0$

$= (x - 5)(x - 40) = 0$

$x = 5,\; 40$

The break-even points are $x = 5$ and $x = 40$.