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Home » Thus, the smallest positive integer \( n \) is: - 500apps

Thus, the smallest positive integer \( n \) is: - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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The cost per unit is \( P(x) = \frac{C(x)}{x} = \frac{5000 + 120x - 0....
To minimize \( P(x) \), take the derivative:
P'(x) = -\frac{5000}{x^2} + 0 - 0.5 = -\frac{5000}{x^2} - 0.5
Set \( P'(x) = 0 \):
-\frac{5000}{x^2} - 0.5 = 0 \Rightarrow \frac{5000}{x^2} = -0.5
This yields a negative right-hand side, which is impossible. But note:...
P'(x) = -\frac{5000}{x^2} - 0.5
This is always negative, meaning \( P(x) \) is decreasing? But that ca...
Actually,
P(x) = \frac{5000}{x} + 120 - 0.5x

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