Soluciontarea1tecvirtualmetodosoptimizacion

Tarea 1 
:: Redacción :: 
Instrucciones. Resolver los siguientes problemas. 
Problema 1 (extraído del libro de texto, problema 4, página 55)
Truckco manufactures two types of trucks: 1 and 2. Each truck must go through the painting shop and assembly shop. If the painting shop were completely devoted to painting Type 1 trucks, then 800 per day could be painted; if the painting shop werecompletely devoted to painting Type 2 trucks, then 700 per day could be painted. If the assembly shop were completely devoted to assembling truck 1 engines, then 1,500 per day could be assembled; if the assembly shop were completely devoted to assembling truck 2 engines, then 1,200 per day could be assembled. Each Type 1 truck contributes $300 to profit; each Type 2 truck contributes $500. Formulate anLP that will maximize Truckco’s profit.

Problema 2 (extraído del libro de texto, problema 4, página 114)
Sunco processes oil into aviation fuel and heating oil. It costs $40 to purchase each 1,000 barrels of oil, which is then distilled and yields 500 barrels of aviation fuel and 500 barrels of heating oil. Output from the distillation may be sold directly or processed in the catalyticcracker. If sold after distillation without further processing, aviation fuel sells for $60 per 1,000 barrels, and heating oil sells for $40 per 1,000 barrels. It takes 1 hour to process 1,000 barrels of aviation fuel in the catalytic cracker, and these 1,000 barrels can be sold for $130. It takes 45 minutes to process 1,000 barrels of heating oil in the cracker, and these 1,000 barrels can be sold for$90. Each day, at most 20,000 barrels of oil can be purchased, and 8 hours of cracker time are available. Formulate an LP to maximize Sunco’s profits.

Problema 3 (extraído del libro de texto, problema 7, página 114)
Steelco manufactures two types of steel at three different steel mills. During a given month, each steel mill has 200 hours of blast furnace time available. Because of differencesin the furnaces at each mill, the time and cost to produce a ton of steel differs for each mill. The time and cost for each mill are shown in Table 48. Each month, Steelco must manufacture at least 500 tons of steel 1 and 600 tons of steel 2. Formulate an LP to minimize the cost of manufacturing the desired steel.

Problema 4 (extraído del libro de texto, problema 14, página 115)
Furncomanufactures tables and chairs. Each table and chair must be made entirely out of oak or entirely out of pine. A total of 150 board ft of oak and 210 board ft of pine are available. A table requires either 17 board ft of oak or 30 board ft of pine, and a chair requires either 5 board ft of oak or 13 board ft of pine. Each table can be sold for $40, and each chair for $15. Formulate an LP that can be usedto maximize revenue.

Maestría en Sistemas de Calidad y Productividad            Métodos de Optimización para la Toma de Decisiones 

 

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:: SOLUCIÓN:: versión en español
Problema 1 (extraído del libro de texto, problema 4, página 55)

Variables de decisión x1 = x2 = Número de camiones tipo 1 fabricados diariamente. Número de camiones tipo 1 fabricados diariamente. Funciónobjetivo Max z = 3x1 + 5x2 utilidad expresada en cientos de dólares. Restricciones x1/800 + x2/700  1 x1/1500 + x2/1200  1 x1, x2  0   (Restricción de pintado) (Restricción de ensamblado del motor) (Restricción de no-negatividad)

Problema 2 (extraído del libro de texto, problema 4, página 114)

Variables de decisión
OIL = miles de barriles comprados de aceite. HOS = miles de barrilesvendidos de aceite combustible no desintegrado. HOP = miles de barriles procesados de aceite combustible, adicionales. AFS = miles de barriles vendidos de combustible no-desintegrado para aviones. AFP = miles de barriles procesados de combustible para aviones, adicionales.

Función objetivo Max z = 40HOS + 90HOP - 40(OIL) + 130AFP + 60AFS Restricciones OIL  20 0.5(OIL) = AFS + AFP 0.5(OIL) = HOS +...