Metodo Simplex

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APUNTES SOBRE EL MÉTODO SÍMPLEX DE PROGRAMACIÓN LINEAL Adriel R. Collazo Pedraja

2 INTRODUCCIÓN Este trabajo tiene como propósito proveer ayuda al estudiante para que pueda comprender y manejar más efectivamente el método símplex de programación lineal. Ilustraremos la aplicación a situaciones de maximización, minimización y análisis de sensibilidad. El Método Símplex como herramienta de programación lineal fue desarrollado para la época de los años cuarenta por George Dantzing, un joven matemático. El método constituye una forma sistemática y de búsqueda intensiva a través de todas las posibles soluciones para obtener una solución óptima. Ello resulta de gran utilidad debido a su eficiencia. Además es fácil programarlo en una computadora. En contraste con el análisis gráfico, este método permite el uso de muchas variables. También permite la aplicación de cantidades de restricciones lineales con signos; mayores e igual, menores e igual y de igualdad. En comparación con el método gráfico, el método símplex tiene como punto de partida el origen siendo este la solución inicial al problema. El método prueba todos los puntos extremos gráficos aunque no necesariamente se detiene en todos los vértices. Por otro lado utiliza el concepto de álgebra de matrices en una serie de tablones. EL PROBLEMA DE MAXIMIXACIÓN SÍMPLEX FORMULACIÓN INICIAL Utilizando el siguiente ejemplo estableceremos la formulación inicial símplex y demostraremos la mecánica del método y su interpretación. El gerente de la Relojería la Torre desea conocer la ganancia máxima que se puede obtener de la producción y venta de dos clases de relojes económicos digitales de pulsera. La ganancia que se obtiene por la producción y venta de un reloj de hombre es de $4 y de $6 para un reloj de mujer. La empresa cuenta con 120 horas semanales para la producción de los relojes y 100 horas para la inspección y empaque de estos. La fabricación de un reloj de hombre requiere 2 horas de producción y 2 horas de

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