Un projet d'énergie renouvelable nécessite une frontière rectangulaire avec un périmètre fixe de 200 mètres. La longueur doit être le double de la largeur. Quels sont les dimensions qui maximisent la superficie de la frontière ?
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- Définissez la dérivée à zéro : \(-4p + 200 = 0 \Rightarrow p = 50 \).
- Le prix optimal est \( p = 50 \).
- #### \( p = 50 \)
- Soit la largeur \( w \) et la longueur \( 2w \).
- Contrainte du périmètre : \( 2(w + 2w) = 200 \Rightarrow 6w = 200 \Rightarrow w = rac{200}{6} = rac{100}{3} \).
- Longueur \( l = 2w = rac{200}{3} \).
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We start by setting up the equation for the concentration: