Model 16: Production Planning

A certain corporation has three branch plants with excess production capacity. All three plants have the capability for producing a certain product, and management has decided to use some of the excess production capacity in this way. This product can be made in three sizes -- large, medium, and small -- that yield a net unit profit of $385, $330, and $275, respectively. Plants 1, 2, and 3 have the excess labor and equipment capacity to produce 750, 900, and 450 units per day of this product, respectively, regardless of the size or combinations of sizes involved. However the amount of available in-process storage space also imposes a limitation on the production rates. Plants 1, 2, and 3 have 13,000, 12,000 and 5,000 square feet of in-process storage space available for a day's production of this product. Each unit of the large, medium, and small sizes produced per day requires 20, 15, and 12 square feet, respectively.

Sales forecasts indicate that 900, 1200, and 750 units of the large, medium, and small sizes, respectively, can be sold per day.

To maintain a uniform work load among the plants and to retain some flexibility, management has decided that the additional production assigned to the respective plants must use the same percentage of their excess labor and equipment capacities.

Management wishes to know how much of each of the sizes should be produced by each of the plants to maximize profit.