P* = $512.36 (profit maximizing price) 7) Max f(Q) = PQ TC(Q) – = 100Q - 8Q2 (50 + 80Q 10Q2 + 0.6Q3) – – = 20Q + 2Q2 0.6Q3 50 – – = 20 + 4Q 1.8Q2 – = 20 + 4Q 1.8Q2 = 0 – Q1 = -2.40 Q2 = 4.62 Thus maximize profit = 20Q + 2Q2 - 0.6Q3 - 50 = 20 (4.62)2 0.6 (4.62)3 50 – – = 317.72 PQ = 100Q 8Q2 – = 100 (4.62) 8(4.62)2 – = 291.24
P* = $512.36 (profit maximizing price) 7) Max f(Q) = PQ – TC(Q) = 100Q - 8Q2 – (50 + 80Q – 10Q2 + 0.6Q3) = 20Q + 2Q2 – 0.6Q3 – 50 = 20 + 4Q – 1.8Q2 = 20 + 4Q – 1.8Q2 = 0 Q1 = -2.40 Q2 = 4.62 Thus maximize profit = 20Q + 2Q2 - 0.6Q3 - 50 = 20 (4.62)2 – 0.6 (4.62)3 – 50 = 317.72 PQ = 100Q – 8Q2 = 100 (4.62) – 8(4.62)2 = 291.24