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Mathematical Model. Linear Programming.

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Ejercicios de programación lineal para resolver mediante el método gráfico.

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Mathematical Model. Linear Programming.

  1. 1. Modelos Matematicos. 1 G.EdgarMataOrtiz. 2014 ModelosMatemáticos: ProgramaciónLineal En el estudio de modelos matemáti- cos de cualquier naturaleza, es ne- cesario resolver ejercicios. Este documento contiene algunos problemas para practicar el método gráfico.
  2. 2. Modelos Matematicos. 2 Resuelve los siguientes modelos por el método gráfico.Problemas: Modelosparapracticarelmétodográfico. 1 2 3 4 5 6 7
  3. 3. Modelos Matematicos. 3 Desarrolla los modelos siguientes y resuélvelos por el método gráfico.Problemas: Plantealosmodelosyresuélvelosporelmétodográfico. Problemas de minimización. 1 En la granja “Gloria Angélica” se usa diariamente un mínimo de 650 kg de un alimento especial que es una mezcla de maíz y soya. Por cada kg de maíz se aportan 0.09 kg de proteínas y 0.02 de fibras, mientras que con la soya se aportan 0.60 kg de proteínas y 0.06 de fibras. El costo del kg de soya es de $0.90 y el de maíz, $0.30. Las necesidades dietéticas son un mínimo del 35% de proteínas y un máximo del 8% de fibra. Gloria Angélica desea determinar la mezcla que, al mismo tiempo que satisface las necesidades dietéticas, reduce los costos. 2 Una campaña para promocionar los productos lácteos “Eli Hernández” se basa en el reparto gratuito de yogures con sabor a limón o a fresa. Se decide repartir al menos 30,000 yogures. Cada yogurt de limón necesita para su elaboración 0.5 gr. de un producto de fermentación y cada yogurt de fresa necesita 0.2 gr. de ese mismo producto. Se dispone de 9 Kg de ese producto para fermentación. El coste de producción de un yogurt de fresa es doble que el de un yogurt de limón. ¿Cuántos yogures de cada tipo se deben producir para que el costo de la campaña sea mínimo? 3 La “Juan Guevara Oil Company” construye una refinería para elaborar cuatro productos; diésel, gasolina, lubricantes y combustible para aviones. Las demandas (en barriles/día) de estos productos son 13000, 30000, 10000 y 11800 respectivamente. Irán y Dubái tiene contrato para enviar el petróleo crudo a la compañía. Debido a las cuotas de producción que especifica la OPEP, la nueva refinería debe recibir al menos el 40% del petróleo crudo de Irán y el resto de Dubái. Las distintas especificaciones de los dos crudos determinan proporciones distintas de productos, un barril de crudo de Irán rinde 0.2 barriles de diésel, 0.25 barriles de gasolina, 0.1 barriles de lubricante y 0.15 de combustible para avión. Los rendimientos correspondientes de del petróleo crudo de Dubái son; 0.1, 0.6, 0.13 y 0.1 respectivamente. Determina la capacidad mínima de la refinería en barriles de crudo por día. 4 El plato favorito de Guadalupe Vitela es la carne con papas. Por eso decidió hacer una dieta continua de sólo estos dos alimentos (más algunos líquidos y suplementos) en todas sus comidas. Guadalupe sabe que no es la dieta más sana y quiere asegurarse que toma las cantidades adecuadas de los dos alimentos para satisfacer los requerimientos nutricionales. Cuenta con la siguiente información: Cada porción de Carne le proporciona 5 gramos de carbohidratos, 20 de proteínas y 15 de grasa; cada porción de papas le proporcionan 15 gramos de carbohidratos, 5 de proteínas y 2 de grasa. Guadalupe quiere determinar el número de porciones diarias (pueden ser fraccionarias) de carne y papas que cumplirían con el requerimiento mínimo diario; 50 gramos de carbohidratos, 40 de proteínas y 60 de grasa. Se desea minimizar el costo sabiendo que el costo por cada porción de carne es de $4 y de papas es de $2. 5 Damián Spíndola está tratando de seleccionar la combinación más barata de dos alimentos, que deben cumplir con ciertas necesidades diarias de vitaminas. Los requerimientos vitamínicos son por lo menos 40 unidades de vitamina W, 50 unidades de vitamina X y 49 unidades de vitamina Y. Cada onza del alimento A proporciona 4 unidades de vitamina W, 10 unidades de vitamina X y 7 unidades de vitamina Y; cada onza del alimento B proporciona 10 unidades de W, 5 unidades de X y 7 unidades de Y. El alimento A cuesta 5 pesos/kilogramo y el alimento B cuesta 8 pesos/kilogramo.
  4. 4. Modelos Matematicos. 4 Bibliografía y páginas web acerca de programación lineal. Referencias: Fuentesdeinformaciónacercadeprogramaciónlineal. Referencias. 1 Operations Research. An Introduction (9th Edition). Hamdy A. Taha 2 Operations Research. Applications And Algorithms. Wayne L. Winston 3 Investigación de Operaciones en la Ciencia Administrativa. Eppen, Larry R. Weaterford and Jeffrey H. Moore. 4 http://fisher.osu.edu/~croxton.4/tutorial/ Tutorial acerca de programación lineal. 5 Free Linear And Mixed-Integer Programming Solvers. Herramientas, gratuitas y de pago, para resolver problemas de Programación Lineal y Programación Entera. 6 Finite mathematics utility: simplex method tool http://www.zweigmedia.com/RealWorld/simplex.html Excelente herramienta a la que se le proporciona el modelo y nos presenta la solución.

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