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mr Goodwill [35]
3 years ago
7

Al precio de p dólares por unidad, se venden x unidades de cierto artículo al mes en el mercado con p=50-0.5x ¿Cuántas unidades

como mínimo se deben vender cada mes con el objetivo de tener ingresos de por lo menos de 1.200 dólares?
Mathematics
1 answer:
Ray Of Light [21]3 years ago
3 0

Answer:

Se debe vender un mínimo mensual de 40 artículos para tener un ingreso mínimo de 1.200 dólares.

Step-by-step explanation:

De acuerdo con el enunciado, x es la cantidad mínima de artículos a un precio de p. Además, los ingresos totales deben ser de un mínimo de 1200. En consecuencia, tenemos el siguiente sistema de ecuaciones:

x \cdot p = 1200 (1)

p = 50-0.5\cdot x (2)

Aplicando (2) en (1), tenemos la siguiente ecuación polinómica:

x\cdot (50-0.5\cdot x) = 1200

50\cdot x -0.5\cdot x^{2} = 1200

0.5\cdot x^{2}-50\cdot x +1200 = 0 (3)

Por la Fórmula de la Cuadrática tenemos las raíces del polinomio:

x_{1} = 60, x_{2} = 40

De acuerdo con el resultado anterior, se debe vender un mínimo mensual de 40 artículos para tener un ingreso mínimo de 1.200 dólares.

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