An introduction to numerical analysis

in emphasis. They discuss the mathematical theory of linear programming ; this includes the definition of basic solutions, duality and the conditions for feasibility and optimality. The authors formulate the primal and dual problems and demonstrate the economic significance of the dual variables. The rules of the simplex method and the method of artificial variables are fully explained and described. The transportation problem is used as an example of a linear program whose structure enables it to be easily solved and finally there is a discussion of game theory and its relationship to linear programming. Throughout both texts there are examples and at the end of each chapter there are exercises. The solutions to the exercises and a suggested reading list are given at the end of each book. The emphasis in Trustrum's book is on the mathematics of linear programming. In this compact little book the author's aim is to prove the important theorems and show their use briefly, but adequately, in a calculation. As such it will be of interest to mathematicians and to those who have had a little practice in formulating linear programs and wish to know about the mathematics of the subject. Walsh, in a longer book, covers the same ground and more in greater detail but without neglecting the mathematical aspects of the subject. For instance not only is it pointed out that the assignment problem can be formulated as a transportation problem but there is a discussion with examples of the " Hungarian " method of solution. The dual simplex and revised simplex methods are discussed in detail and there is a section on sensitivity analysis. The author shows how a problem can be formulated as a linear program and in the exercises there are some formulations to be done by the reader. The author has struck a good balance between the theoretical aspects of linear programming and the need to demonstrate how the solution to a problem may be computed. This book is recommended to those who want a clear account of linear programming and to those who have read a shorter book and wish to increase their knowledge without plunging into a substantially longer text.