*Elements of Linear Programming with Economic Applications*has a second edition which appeared in 1973 but with authors R C Geary and J E Spencer. Reviewers are fairly critical (in some cases extremely critical) of Geary's two main texts, as the reader will see from the extracts below.

**1. Tests of Normality (1938), by R C Geary and E S Pearson.**

**1.1. Review by: W G Madow.**

*Journal of the American Statistical Association*

**33**(203) (1938), 622-623.

The monograph is clearly and non-mathematically written. References are given to the theoretical research on which it is based. It makes available, for routine computation, statistical methods which, in that they are easy to use and are valid for samples of any size, are superior to the techniques now commonly employed for the same purpose.

**1.2. Review by: H L S.**

*Journal of the Institute of Actuaries (1886-1994)* **69** (1) (1938), 101.

The reaction from the normal curve which was due, in the main, to Karl Pearson's contributions to the theory of frequency curves, has now given place to a wide application of statistical methods which depend for their validity on the hypothesis of a normal universe. This being the case, it becomes of great importance to test whether statistics actually observed can reasonably be assumed to have originated from some normal universe or, rather, whether they exhibit any definite signs of non-normality. The present tables supply a means of testing the latter hypothesis ...

**2. Elements of Linear Programming with Economic Applications (1964), by R C Geary and M D McCarthy.**

**2.1. From the Preface.**

After fairly surveying the economic context, the Authors consider that a short work like this is needed, since they have found that when the treatment is mathematical, there tend to be unnecessary incursions into matrix algebra, while in economic textbooks economic principles are prone to get mixed up with the mathematics, thus obscuring the lines of solution. So here is yet another attempt, in which any merit it possesses can be only in the manner of presentation.

**2.2. Review by: E M L Beale.**

*Journal of the Royal Statistical Society. Series A (General) ***128** (1) (1965), 148.

In the foreword to this monograph the authors explain that their objective was to describe what linear programming is about, and how to solve easy problems using the simplex method. They have particularly in mind the needs of students of economics who dislike unnecessary incursions into matrix algebra. The first part of the book is called Theory. In it the geometry of the simplex method is clearly explained, but the algebraic treatment is less satisfactory. It is nowhere clearly stated that each tableau is a representation of the original problem with the equations solved for the basic variables in terms of the non-basic variables, so that only a simple change of variable (Jordan elimination) is involved in progressing from one tableau to the next. The introduction of non-standard terminology is also unfortunate. ... To sum up, this is a pleasantly written book, but it takes too little note of the developments in the subject over the last ten years.

**2.3. Review by: W R Buckland.**

*Biometrika* **52** (3/4) (1965), 671-672.

The drafting of this monograph is as clear and crisp as would be expected from its authors and there is little doubt that it will be most helpful introductory material for a wide range of students in the general field of economics and business management. Indeed, they will quickly appreciate the close relationship between basic economic principles and mathematical programming techniques as a means for investigating their practical consequences. What is not so clear, however, is where these readers will turn after mastering this short exposition. Apart from some footnotes to give certain credits in Part 2, there is no guide to further reading whatsoever. However, this monograph can be warmly recommended for those specially interested in economic applications of linear programming

**2.4. Review by: F Conway.**

*The Mathematical Gazette* **50** (371) (1966), 86-87.

Dr Geary and Dr McCarthy have written for those who want to know what linear programming is about and how to solve easy problems using the Simplex method. An elementary explanation of basic principles is followed by more complex examples and the application of these methods to a number of economic problems, such as the best use of machinery within a firm, or the most profitable allocation of farming resources among agricultural products.

**2.5. Review by: A Land.**

*Economica, New Series* **33** (132) (1966), 496.

The whole emphasis of the booklet is on teaching the student to perform the simplex calculations. Perhaps rather unfashionably, I would agree that this is a useful exercise, even for the intending practitioner whose inclination is to leave it all to the electronic computer. It is less convincing that one needs to work on a desk calculator in order to acquire the necessary insight. The assumption appears to be that the reader will be driven to carry out his actual calculations on real data in this way, which must be rather rare in these days. On the whole, it gives a clear exposition, and gives due weight to the sort of difficulties which students encounter. It would be grossly unfair to fault it for its omissions

**2.6. Review by: C A Trauth.**

*Technometrics* **7** (3) (1965), 453.

This book is written primarily for persons with little technical training who are interested in obtaining some understanding of and facility with the Simplex algorithm. It is basically a text that teaches by example without, however, neglecting rigor as often happens in such books. The examples deal with economic situations (as the title of the book implies), but the authors wisely avoid the use of economic concepts such as "shadow prices," "opportunity cost," and so forth as aids for teaching students of economics, making the text suitable for use by persons unfamiliar with these terms.

**2.7. Review by: C van de Panne.**

*Revue de l'Institut International de Statistique / Review of the International Statistical Institute* **33** (3) (1965), 561.

There exists already a number of books on linear programming at the elementary level, but there is so much interest in the subject that yet another book should be welcomed. After all, it may be that different books catch the fancy of different sorts of readers. Rather crucial in such an elementary work on linear programming is to explain the Simplex Method by means of a simple example. The authors have recognised this and before the somewhat more formal exposition they give such an example. However, the treatment of this example is not at all clear and the student beginning this subject may find it rather confusing ... Throughout the book any references to the extensive literature on mathematical programming are missing, except for the various examples taken from other works; this is a serious deficiency for an introduction, which should at least indicate where to find more advanced work. If the book had appeared some 7 to 10 years ago (with original examples) it would have been received more favourably, but at the present state of the subject it is somewhat disappointing. Nevertheless, the economist may find it useful, if only for a different treatment and interpretation of the examples of application.

**2.8. Review by: M L Balinski.**

*Mathematical Reviews*, MR0168373 **(29 #5636).**

This short, inexact, and often misleading book is intended to be an introduction to linear programming for students of economics. The book fails in presenting both "theory" and "applications". Part I, "Theory", begins by considering a simple example which is solved graphically and by a labored use of a simplex method. There follows a general discussion of the linear programming problem and a simplex method for its solution. However, this discussion is misleading, and contains false statements, together with erroneous proofs. Duality is treated as a mystical gift ...

**3. Exercises in mathematical economics and econometrics (1974), by J E Spencer and R C Geary.**

**3.1. Review by: P Hudson.**

*The Mathematical Gazette*

**59**(409) (1975), 211-213.

This volume is written for third-year undergraduates and first-year post-graduate students. Each of the six chapters is divided into three parts: theory; exercises-about twenty of them in each chapter; and the third part, answers to the exercises, is unusual in that the solutions to the more difficult problems are presented in considerable detail and thereby enhance the opportunity for the student to work on his own. ... The conception of this book is an excellent one and, overall, its execution deserves high praise. Apart from its stated market, this volume may also be of benefit to those sixth form teachers of mathematics who have a casual interest in the social sciences.

**3.2. Review by: G E Mizon.**

*Journal of the Royal Statistical Society. Series A (General)* **139** (1) (1976), 137-138.

This book, which is aimed at final-year undergraduates or graduates studying mathematical economics and econometrics, contains chapters on classical optimization theory, linear and nonlinear programming, games theory, multiple regression and simultaneous equations. Each chapter has a review of relevant theory, together with a set of exercises and companion solutions, at varying levels of difficulty. Hence the form of the book appears to be consistent with the authors' intention of guiding readers to a deeper understanding of the subjects via carefully chosen examples. Unfortunately, the reviews of theory are not unqualified successes, especially the two on econometrics. Since the book cannot be used independently of mathematical economics and econometrics textbooks, the theoretical reviews, if they are not to be redundant, should be significant enough in their own right to justify a separate text. Otherwise the theoretical points to be emphasized could be better presented through the exercises and answers. In fact, the theoretical reviews are occasionally incorrect or misleading.