Find the maximum profit that a company can make, if the profit function is given by $P(x) = 72 + 42x - x^2$, where $x$ is the number of units and $P$ is the profit in rupees.

513

The correct answer is Option (2) → 513 ##

For maxima and minima, $P'(x) = 0 \Rightarrow 42 - 2x = 0 \Rightarrow x = 21$ and $P''(x) = -2 < 0$.

So, $P(x)$ is maximum at $x = 21$.

The maximum value of $P(x) = 72 + (42 \times 21) - (21)^2 = 513$

i.e., the maximum profit is ₹513.