GATE 2025 Question 45: Monopolistic competition and oligopoly

Consider a three-firms oligopoly market with a linear demand function given by

$P = 25 - Q$

where $P$ is the unit price and $Q$ is the total quantity supplied.

The total quantity $Q = (q_1+q_2+q_3)$, where $q_i$ is the output from the $i^{th}$ firm with $i=1,2,3$.

The total cost (TC) curve of firm $i$ is given by $TC_i = (\alpha_i + 5q_i)$, where $\alpha_i$'s are positive real numbers.

Assuming a Cournot solution exists, the value of $Q$ is