6. A firm uses a single plant with costs C = 160 + 16Q + .1Q2 and faces the price equation P = 96 - .4Q.a. Find the firm's profit-maximizing price and quantity. What is its profit? MR = 96 - .8Q MC = 16 + .2Q 96 - .8Q = 16 + .2Q 80 = Q P = 96 - .4(80) P = 64 Profit = 80(64) - 160 - 16(80) - .1(80)^2 = 3040 The firm's production manager claims that the firm's average cost of production is minimized at an output of 40 units. Furthermore, she claims that 40 units is the firm's profit-maximizing level of output. Explain whether these claims are correct. AC = 160/Q +16 +.1Q To minimise this dAC/dQ = 0 =-160/Q2 +.1 Or Q = 40 But at this level profits are not maximised. This happens at Q= 80 only. So the claims are right about AC being maximised, but not profit maximisation level of Q Could the firm increase its profit by using a second plant (with costs identical to the first) to produce the output in part (a)? Explain