Empowering users with the knowledge necessary to begin using mathematical programming as a tool for managerial applications, this practical text shows when a mathematical model can be useful in solving a problem, and instills an appreciation and understanding of the mathematics associated with the applied techniques. Surveys problem types, and discusses various ways to use specific mathematical tools. Contains a brief introduction to matrix algebra as prerequisite material for the study of linear programming. The discussion of linear programming includes a verification of the simplex algorithm and a chapter on duality and sensitivity analysis. Discusses the special structures of four network problems: the transportation problem, the critical path method, the shortest path problem, and minimal spanning trees. Includes the method of Lagrange multipliers for non-linear optimization. Touches on "mathematics" oriented (vs. applications) material, with integrated proofs and discussions on such topics as basic graph theory, matrix algebra, and properties of algorithms. Appendices include answers to the odd problems, an introduction to the linear programming software LINDO, an overview of the symbolic computation package Maple, and a brief introduction to Excel and its optimization add-in Solver.