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 =0.033Q2 + 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.