The total cost and the total revenue of a company that produces and sells x units of particular product are respectively $C(x) = 5x + 350$ and $R(x) = 50x – x^2$. Find the values of $x$ that produce a profit.

$10<x<35$

The correct answer is Option (4) → $10<x<35$

For profit, $R(x) > C(x) = 50x - x^2 > 5x + 350$

$⇒ x^2 - 45x + 350 <0 ⇒ (x-10) (x -35) <0$

$⇒ 10 < x < 35$.