GATE 2025 Question 42: Monopoly and price discrimination

The inverse demand function for a monopolist is given by

$P = 100 - kQ$

where $P$ is the unit price of the good, $Q$ is the quantity and $k$ is a constant.

The cost function facing the monopolist is given as $C(Q) = 50 + 2Q(1+Q)$.

If the profit maximizing output is 7, the maximum profit is ______ (in integer)