Your firm has a cost function C=6+4Q+Q^2. (The corresponding average cost function is AC=(6/Q)+4+2Q and the corresponding marginal cost function is MC = 4+2Q).
(i) What is the optimal ouput if the price of your product is constant at P=20?
(ii) Now suppose that price is not constant but the demand for your product is given by Q=12-P or equivalently P=12-Q. (The corresponding total revenue function is TR=12Q-Q^2 and the marginal revenue function is MR=12-2Q). Now what is your optimal output?