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Linear Programming 1: Introduction by G.B. Dantzig and M.N. Thapa Springer, 1997. ISBN 0-387-94833-3, hb.
This is a promptly scheduled book from the founder of Linear Programming (LP) and one of his former students for the 50th birthday of the simplex method. The declared aim of the authors is to provide an easy introduction on the undergraduate level to the algorithms and applications of LP. No more than some elementary linear algebra is assumed as prerequisite. The proofs of deeper mathematical results are postponed to Linear Programming 2, the second volume. However, contrary to several other introductory undergraduate LP books, the importance of the mathematical results is emphasized here. The reader finds carefully formulated definitions and theorems.
Before going into detailed discussions, we can certify that the goal of the authors is met. The book is easily accessible, written with care, and the reader profits from George Dantzig's 50 years research and teaching experience. The results, algorithms are illustrated with a large number of examples. Each chapter closes with a short discussion of the literature and a rich collection of exercises.
It is always exciting to learn from the most authentic source how the story of LP and the simplex method began. This is the content of...