The demand function of a monopolist is $q = 12 - p$ where $p$ is the price. Using the total cost and total revenue I was trying to calculate the optimal (short term) level of production.
I tried to solve it using the total revenue $r = p x$. Then I calculated the marginal revenue (the derivative of total revenue) and set it to $0$. Then I got $p = 6$ and $x = 6$.
However, I never used the cost function, what did I do wrong?