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But as \( x \to 0^+ \), \( 5000/x \to \infty \); as \( x \to \infty \), \( -0.5x \to -\infty \), but \( 5000/x \to 0 \), so \( P(x) \to -\infty \)? That's impossible.
Likely a typo in interpretation. For realistic models, average cost typically has a minimum.
But given: \( C(x) = 5000 + 120x - 0.5x^2 \). This implies fixed startup cost 5000, linear marginal cost 120, but reduced fixed cost at higher volume — unusual.

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