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Answer #1 | 26/12 2013 14:55

C(q) = 0.01q^3 - 0.6q^2 + 13q + 1 R(q) = 8q P(q) = R(q) - C(q) = 8q - (0.01q^3 - 0.6q^2 + 13q + 1) = -0.01q^3 + 0.6q^2 - 5q - 1 so P'(q) = -0.03q^2 + 1.2q - 5 ← power rule 0 = -0.03q^2 + 1.2q - 5 solve with quadratic formula: q ≈ 4.72 or q ≈ 35.28 thus P(4.72) ≈ -12.28 P(35.28) ≈ 130.28 so max profit ≈ $130 .

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