a f xy 3x 2 4y 2 15 si 4x y 67 b f xy x 3 y 3 si 6x 12y 72 c f xyz x 2 y 2 z 2

A f xy 3x 2 4y 2 15 si 4x y 67 b f xy x 3 y 3 si 6x

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multiplicadores de Lagrange. a . f ( x,y )= 3x 2 + 4y 2 15 si 4x + y = 67 b . f ( x,y )=− x 3 y 3 si 6x + 12y = 72 c . f ( x,y,z )= x 2 + y 2 + z 2 si x + y + z = 11 y x + y z = 5 Página 7 de 8 © Escuela Bancaria y Comercial, S.C.
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6. La producción de una pyme depende de dos insumos: A y B. La expresión P ( x, y )= x 0.7 y 0.3 representa la función de producción, donde X corresponde al número de unidades del insumo A mientras que Y a la cifra del insumo B. a. Determina la cantidad de unidades que la empresa debe comprar de cada insumo, para alcanzar una producción máxima. Toma en cuenta que no hay ninguna restricción que cumplir. Interpreta el resultado. b. Supón que el precio unitario del insumo A equivale a $100.00 y el de B a $120.00; el departamento de finanzas autorizó un presupuesto de $500,000.00 para la compra de tales recursos. Determina, con base en la información proporcionada, la cantidad de insumos que la empresa debe comprar para maximizar la producción. Página 8 de 8 © Escuela Bancaria y Comercial, S.C.
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