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:
Answer & explanation
Correct answer: option 2
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 $x = 40$.