Note on Linear Programming: A Brief Overview

In some situations, the available resources are adequate to carry out the alternative operating plan selected. In others, however, this is not true. For example, a machine has only a certain amount of capacity. If that capacity is entirely used by one product, it cannot be used for another. Similarly, a factory building has room for only so many machines. In these situations, there are constraints on the uses of resources. Linear programming is a model for solving problems that involve several constraints. In it, a series of linear mathematical relationships is developed. The first, called the objective function, is the quantity to be optimized. This is usually a formula for differential costs, which the model will minimize, or one for differential income, which is to be maximized. The other statements express the constraints of the situation.

• Use linear programming to determine constraints.
• Identify areas of highest contribution.
• Calculate a shadow price for each constrained resource.