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P'(x) = -\frac{5000}{x^2} - 0.5 \quad \text{— still negative?}
Wait — no, derivative of \( -0.5x \) is \( -0.5 \), derivative of \( 5000/x \) is \( -5000/x^2 \), so total:
This is always negative, meaning cost per unit decreases as \( x \) increases? But the model \( C(x) = 5000 + 120x - 0.5x^2 \) is only positive for \( x < 250 \), and the current version increases linearly in cost, but quadratic loss? Actually, the cost function models *reducing* average cost? Let's reconsider.

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