I have a cost minimization objective function with 4 decision variables: Q, Pi-x, L and n (equation 5).

The L and n would be set with an initial value of their range in the iterative algorithm. But I have a problem to get to optimal value of Q and Pi-x. Actually the equation I got for Q is too much complicated and the Q are in both sides (equation 9).

Also the Pi-x equation includes the Q.

Can anyone help me how can I get to the optimal solution of Q and Pi-x considering that all the other terms (including L and n) are known?

Thanks