Linear programming and its generalization, mathematical programming, can be viewed as part of a great revolutionary development that has given mankind the ability to state general goals and lay out a path of detailed decisions to be taken in order to best achieve these goals when faced with practical situations of great complexity. The tools for accomplishing this are the models that formulate real-world problems in detailed mathematical terms, the algorithms that solve the models, and the software that execute the algorithms on computers based on the mathematical theory.
Our goal then is to provide a simple introduction to these various tools in the context of linear programming. Because this is an introduction to the field at the Undergraduate level, no proofs of key ideas are provided except for a few that are easy to follow. We prefer to state the key ideas as theorems and lemmas, rather than as facts or properties, as is done in some introductory texts because we wish to highlight the importance of the mathematical results. Examples are provided to illustrate the main ideas. Proofs of all the theorems and lemmas can be found in Linear Programming
2. Selected bibliographical references can be found at the end of each chapter.
We assume that the reader has some knowledge of elementary linear algebra. For those whose knowledge is weak or non-existent, necessary details on linear algebra used in this text are provided in the appendices.