Métodos de optimización para la toma de decisiones

1.- Gepbab Corporation produces three products at two different plants. The cost of producing a unit at each plant is shown in Table 6. Each plant can produce a total of 10,000 units. At least 6,000units of product 1, at least 8,000 units of product 2, and at least 5,000 units of product 3 must be produced. To minimize the cost of meeting these demands, the following LP should be solved:Here, xij = number of units of product j produced at plant i. Use the LINDO output in Figure 9 to answer the following questions:

a What would the cost of producing product 2 at plant 1 have to be forthe firm to make this choice?

Primero que nada se tendría que agregar una restricción nueva que nos indique esto.

Y ahora la planta 1 solo tendría excedente de 2000 unidades las cuales se leasignarían al producto 1, quedando en la planta 2 4000 unidades producidas de producto 1 y las 5000 del producto 3, elevando el costo a 140,000.

b What would total cost be if plant 1 had 9,000 unitsof capacity?

El costo total sería de 130,000 porque la cantidad faltante se le asignaría a la planta 2 y como el producto 1 se satisface bien de la primer planta al que se le quitaría fuera alproducto tres para surtirlo de la planta dos, aumentando el costo en 2 por unidad.

c If it cost $9 to produce a unit of product 3 at plant 1, then what would be the new optimal solution?

Seguiríasiendo la misma, ya que el análisis de sensibilidad nos indica que podemos incrementar en uno el costo del producto 3 en la planta 1. Pasando de 8 a 9 sin ningún problema.

2.- Giapetto, Inc., sellswooden soldiers and wooden trains. The resources used to produce a soldier and train are shown in Table 11. A total of 145,000 board feet of lumber and 90,000 hours of labor are available. As many as50,000 soldiers and 50,000 trains can be sold, with trains selling for $55 and soldiers for $32. In addition to producing trains and soldiers itself, Giapetto can buy (from an outside supplier)...