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Home » \(n = \frac{-1 \pm \sqrt1681}2\). - Tacotoon

\(n = \frac{-1 \pm \sqrt1681}2\). - Tacotoon

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Wait — perhaps it's \( C(x) = 5000 + 120x - 0.5x^2 \), but \( x \) has an upper limit. But no.

📌 Alternatively, the term \( -0.5x^2 \) may be a typo, and it should be \( +0.5x^2 \). Let's assume that, as it's common in real models.

📌 So assume \( C(x) = 5000 + 120x + 0.5x^2 \). Then average cost:

📌 P(x) = \frac{5000}{x} + 120 + 0.5x

📌 Now take derivative:

📌 P'(x) = -\frac{5000}{x^2} + 0.5

📌 -\frac{5000}{x^2} + 0.5 = 0 \Rightarrow \frac{5000}{x^2} = 0.5 \Rightarrow x^2 = 10000 \Rightarrow x = 100

📌 Since \( x > 0 \), \( x = 100 \).

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