Introduction to Mathematical Programming
Empowering users with the knowledge necessary to begin using mathematical programming as a tool for managerial applications and beyond, this practical guide 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 prerequisite material for the study of linear programming, and offers a brief introduction to matrix algebra. Discusses the special structures of four network problems: the transportation problem, the critical path method, the shortest path problem, and minimal spanning trees. Covers compound interest and explores the financial aspects of specific problems considered throughout the book. Touches on "mathematics" oriented (vs. applications) material, with integrated proofs and discussions on such topics basic graph theory, linear algebra, analysis, properties of algorithms, and combinatorics. An extensive appendix section includes answers to many problems, an introduction to the linear programming package LINDO, an overview of the symbolic computation package Maple, and brief introductions to the TI-82 and TI-92 calculators and their applications.
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Vectors and Matrices
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acres activities artificial variables basic feasible solution basic solution basic variables branch-and-bound calculation Chapter circuit coefficients column concave function consider convex convex function corresponding cost critical path critical point Determine dynamic programming edge entries Example Exercise expression extrema Figure formulation Gauss-Jordan elimination Gaussian elimination graph increase indicates integer program inventory inverse knapsack problem level curves LINDO linear combination linearly independent LINGO Listing Maple matrix Maximize maximum minimal spanning tree minimization problem minimum multipliers needed negative node nonnegative nonzero Note objective function objective function value objective row obtained optimal solution optimal tableau pivot plant positive production profit Proposition replacement quantity resource right-hand side second constraint Section set of feasible simplex algorithm simplex tableau slack variable Solve the following Subject surplus variable system of equations Table Theorem transportation problem traveling salesman problem vertex vertices yields zero