Question

If the demand equation is x+4p=100, calculate the marginal revenue when x=20

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Fred

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Dada la ecuación de demanda x + 4p = 100 Primero, despejamos p : 4p = 100 - x p = \frac{100 - x}{4} Ahora, el ingreso total R se define como R = p \cdot x Sustituyendo la expresión de p : R = \left( \frac{100 - x}{4} \right) x Simplificando: R = \frac{100x - x^2}{4} Para encontrar el ingreso marginal, tomamos la derivada de R con respecto a x : \frac{dR}{dx} = \frac{d}{dx} \left( \frac{100x - x^2}{4} \right) \frac{dR}{dx} = \frac{1}{4} \frac{d}{dx} (100x - x^2) \frac{dR}{dx} = \frac{1}{4} (100 - 2x) Evaluamos la derivada en x = 20 : \frac{dR}{dx} \bigg|_{x=20} = \frac{1}{4} (100 - 2(20)) \frac{dR}{dx} \bigg|_{x=20} = \frac{1}{4} (100 - 40) \frac{dR}{dx} \bigg|_{x=20} = \frac{1}{4} \cdot 60 \frac{dR}{dx} \bigg|_{x=20} = 15 Por lo tanto, el ingreso marginal cuando x = 20 es 15

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