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Problemas De Programación Lineal Essay

1065 words - 5 pages

Investigación de operaciones

2.7.4.
En una carpintería se cuenta con 32 horas de mano de obra. La producción consiste de dos productos: mesas y sillas. Se necesitan 45 minutos para ensamblar una silla y 2 horas para ensamblar una mesa. Se venden por lo menos 4 sillas para cada mesa. El precio de venta es de $100 por mesa y $30 por silla.
Formule un modelo matemático de programación lineal para maximizar los ingresos de la carpintería
Horas 32 | mesas | Sillas |
Tiempo | 2hr | 45´ = 0.75 hr |
Venta | | 4 veces más |
Precio | 100 | 30 |

Variables
X1 Cantidad de mesas a elaborar
X2 Cantidad de Sillas a elaborar

F.0
MaxZ=100x1+30x2

Restricciones:
2X1 + ...view middle of the document...

O.
2.50X1+2.00X2

Restricciones
20X1+10X2≤250
30X1+20X2≤380
15X1≤50
X1+X2 ≤ 6800
X1≥0 Para i≥1,2

2.7.5. Banco
Un banco asignará la cantidad de $80,000 para préstamos de dos tipos: personales y para automóvil. El banco cobra una tasa de interés anual del 14% en préstamos personales y del 12% en préstamos para automóvil. Ambos tipos de préstamos se saldan en periodos de tres años. El monto de los préstamos para automóvil debe ser cuando menos dos veces mayor que el de los préstamos personales. La experiencia anterior muestra que los adeudos no cubiertos constituyen el 1% del importe de todos los préstamos personales. Formule un modelo de programación lineal para determinar cómo deberán asignarse los fondos para maximizar las utilidades del banco.
Asignación | Personales | Autos |
8000 | | 2 veces más |
Cobro | 14% | 12% |
Tiempo | 3 años | 3 años |
Variables
X1 Cantidad de préstamos personales
X2 Cantidad de préstamos para autos

F.O.
Max Z =3(14X1+12X2-1X1)
X1 + X2 ≤ 80,000.00
X2≥2X1
Xi ≥ 0 Para i=1,2

2.7.6.
Una empresa elabora los productos A y B; cada producto A requiere de dos veces más tiempo de mano de obra que el producto B. Si la empresa fabrica exclusivamente productos B puede producir 550 diariamente. La empresa puede vender diariamente un máximo de 200 productos A y 275 productos B. Los precios de venta de los productos A y B son respectivamente de $12 y $8.
Formule un modelo matemático de programación lineal para maximizar los ingresos de la empresa.

Variables
X1 Cantidad de producción y venta de A
X2 Cantidad de producción y venta de B
Max Z= 12x1+8x2
Restricción
X1=2X2
X1 ≤ 200
X2 ≤ 275
Xi ≥ 0 Para i= 1,2

2.7.7

2.7.7
Una empresa fabrica los productos A y B. El volumen de ventas del producto A es cuando menos el 70% de la cantidad total producida. Actualmente, la empresa dispone de 500 kg de materia prima para elaborar A y B. ...

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