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Home » \( 140 - 21 = 119 \). - AMAZONAWS

\( 140 - 21 = 119 \). - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 Therefore, likely the quadratic coefficient is positive. Assume a typo, and the intended model is \( C(x) = 5000 + 120x + 0.5x^2 \). But the problem says \( -0.5x^2 \).

📌 Alternatively, perhaps it's \( C(x) = 5000 + 120x + 0.5x^2 \)? But it says \( -0.5x^2 \).

📌 Given the instructions, we proceed with the **given** function, but realize: to minimize \( P(x) = \frac{5000}{x} + 120 - 0.5x \), take derivative:

📌 Set to zero: no solution. So no critical point — minimum occurs at boundary? But unbounded below? Not physical.

📌 Wait — better: perhaps the cost function is \( C(x) = 5000 + 120x - 0.5x^2 \), and we minimize **total cost**, but the phrase is "cost per unit".

📌 Given the confusion, let's assume the function is meant to be minimized as total cost, but the problem says "cost per unit".

📌 Alternatively, perhaps "cost per unit" is misphrased, and we minimize average cost, but as shown, it has no minimum.

📌 But in business models, average cost \( C(x)/x = 5000/x + 120 - 0.5x \) has a minimum when derivative is zero.

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