Suppose a firm's inverse demand curve is given by P=120 - .5Q, and its cost equation is C = 420 + 60 Q + 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.