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Home » The smallest integer greater than 9.9857 is \(t = 10\). - Portal da AcÃºstica

The smallest integer greater than 9.9857 is \(t = 10\). - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Une entreprise produit des widgets qui circulent sur un marchÃ© avec une courbe de demande donnÃ©e par \( D(p) = 100 - 2p \), oÃ¹ \( p \) est le prix par widget. Le coÃ»t de production pour \( x \) widgets est donnÃ© par \( C(x) = 50x + 200 \). Si l'entreprise souhaite maximiser son profit, quel prix \( p \) devrait-elle facturer par widget ?

📌 D'abord, exprimez \( x \) en fonction de \( p \) : \( x = 100 - 2p \).

📌 La fonction de revenu \( R(p) \) est \( R(p) = p imes x = p(100 - 2p) = 100p - 2p^2 \).

📌 La fonction de profit \( \Pi(p) = R(p) - C(x) \) nÃ©cessite d'exprimer \( C \) en fonction de \( p \) : \( C(x) = 50(100 - 2p) + 200 = 5000 - 100p + 200 \).

📌 Simplifiez pour obtenir : \( \Pi(p) = 100p - 2p^2 - (5200 - 100p) = 100p - 2p^2 - 5200 + 100p \).

📌 Combine les termes : \( \Pi(p) = -2p^2 + 200p - 5200 \).

📌 Pour trouver le maximum, prenez la dÃ©rivÃ©e : \( rac{d\Pi}{dp} = -4p + 200 \).

📌 DÃ©finissez la dÃ©rivÃ©e Ã zÃ©ro : \(-4p + 200 = 0 \Rightarrow p = 50 \).

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