Suppose a firm's inverse demand curve is given by

P = 120 - 0.5Q and its cost equation is

C=420+60Q+Q^2

a. Find the firm's optimal quantity, price and profit 1) by using the profit and marginal profit equations

and 2) by setting MR equal to MC. Also provide a graph of MR and MC.

b. Suppose instead that the firm can sell any and all of its output at the fixed market price P = 120. Find the firm's optimal output.