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An Introduction to Linear Programming and Matrix Game Theory

This book evolved from a course of lectures the author has given at the University of Essex to second year undergraduate social scientists, whose mathematics is generally of O level standard. The book consists of 52 pages of text, 14 pages of problems, 54 pages of solutions and an index. It is therefore suitable for students working on their own, while giving a good basis for lectures to students of modest mathematical attainments. There is a very clear and simple account of the general problem of linear programming and the simplex method in four chapters, then a chapter on the transportation type of problem. Chapters 6 and 7 give the elements of the theory of matrix games, and the last chapter uses the theory of games to introduce the idea of duality in linear programming. The book is an admirable introduction to the subject for non-mathematicians, but there are two small points where an improvement could be made. We are told that Lagrange "tackled the idea of optimising a mathematical function", though the word "optimise" would have puzzled Lagrange and is not defined in the text. Also a job allocation problem is given on p. 62 with suggestions for solving it by transportation techniques. The Hungarian method would solve it much more simply and would interest the reader. These minor criticisms should not obscure the fact that the problems and very full solutions are most instructive, and the book can be confidently recommended.