A firm manufactures and sells a product that has the following demand function: Q = 180 - 4P where P is price, Q is quantity. It also faces the following total cost (TC) function:
TC =0.033Q^{2} + 15Q+150 where Q is quantity produced. (i) Determine the firm's profit function.
(ii) Using your profit function measured in part (i) find the level of output where the firm maximises its profit.