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FromTheMoon [43]
3 years ago
7

1. Un proyecto habitacional Una contratista de viviendas ha subdividido una granja en 100 lotes para construcción. Ella ha diseñ

ado dos tipos de casas para estos lotes: colonial y estilo ranchero. Una casa colonial requiere $30,000 de capital y produce una utilidad de $4000 cuando se venda. Una casa estilo ranchero requiere $40,000 de capital y da una utilidad de $8000. Si la contratista tiene $3.6 millones de capital a la mano, ¿cuántas casas de cada tipo debe construir para obtener máxima utilidad? ¿Quedarán vacíos algunos de los lotes?
Mathematics
1 answer:
Sunny_sXe [5.5K]3 years ago
8 0

Answer:

número de rancho en casa= 90 homes

número de coloniales = 0

Step-by-step explanation:

Deje que el número del colonial sea x

Deje que el número de rancho sea y

Entonces;

30000 x + 40000 y = 3.6 × 10⁶ ---- (1)

x = \frac{3.6*10^6-4*10^4y}{3*10^4}

entonces beneficio P = 30000 x + 8000 y

P = 30000(\frac{3.6*10^6-4*10^4y}{3*10^4})+8000 \ y

\frac{dP}{dy} = \frac{-4*10^4}{3*10}+8000

Para obtener el máximo beneficio; El número de casas de rancho debe ser lo más alto posible:

y = \frac{3.6*10^6}{4*10^4}

número de rancho en casa= 90 homes

número de coloniales = 0

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