Suppose a firm's demand function is given by Q= 240 - 2Pand its cost equation is C = 420 + 60Q + Q².

a. Derive the inverse demand function (1.5 points)

b. Derive the revenue function (1.5 points)

c. Derive the marginal revenue and marginal cost (3 points)

d. Find the firm's optimal quantity, price, and profit 4 points e. 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. 2 points