Cartel profit maximizing quantity question (Cournot game)
Hint

By colluding, presumably the two firms would like to figure out the least costly way to produce in order to maximize profit. Treat the two firms as two production plants of a single "parent company". The total cost of the cartel can then be found by solving 
\begin{equation}
C_\text{cartel}(Q)=\min_{q_1,q_2}\;[C_1(q_1)+C_2(q_2)],\quad\text{s.t.}\quad q_1+q_2=Q.
\end{equation}
This will give you a the optimal way of distributing production across the two firms, $q_i^*(Q)$, as a function of aggregate output $Q$. Then the cartel's total cost is just the sum of the member firms' costs evaluated at the optimum: $C_\text{cartel}(Q)=\sum_i C_i(q_i^*(Q))$.