Many major decisions faced by a manager of a business focus on the best way to achieve the objectives of the firm, subject to the restrictions placed on the manager by the operating environment. These restrictions can take the form of limited resources, such as time, labor, energy, material, or money; or they can be in the form of restrictive guidelines, such as a recipe for making cereal or engineering specifications. One of the most frequent objectives of business firms is to gain the most profit possible or, in other words, to maximize profit. The objective of individual organizational units within a firm (such as a production or packaging department) is often to minimize cost. When a manager attempts to solve a general type of problem by seeking an objective that is subject to restrictions, the management science technique called linear programming is frequently used.
Objectives of a business frequently are to maximize profit or minimize cost .
Linear programming is a model that consists of linear relationships representing a firm's decision(s), given an objective and resource constraints .
There are three steps in applying the linear programming technique. First, the problem must be identified as being solvable by linear programming. Second, the unstructured problem must be formulated as a mathematical model. Third, the model must be solved by using established mathematical techniques. The linear programming technique derives its name from the fact that the functional relationships in the mathematical model are linear , and the solution technique consists of predetermined mathematical stepsthat is, a program . In this chapter we will concern ourselves with the formulation of the mathematical model that represents the problem and then with solving this model by using a graph.