Alligation, Forerunner of Linear Programming

Abstract

IF HERR DOKTOR PROFESSOR GAUSS could read the present-day scientific journals, he would find much evidence that mathematics is, indeed, revered as the queen of science. But he might wonder if we now recognize arithmetic as the queen of mathematics. The modern science of economics, for example, makes much use of matrix inversion, of difference equations, and of other forms of higher mathematics. But arithmetic gets little attention.2 A case in point is linear programming. The methods developed by Dantzig3 and others4 are elegant, but they are hard for the ordinary economist to understand. Several authors5 have tried to help him by publishing simplified explanations of these methods. But perhaps there is another alternative. Perhaps the economist will find that simple arithmetic methods will enable him to solve typical linear programming problems. He doesn't necessarily have to be able to manipulate matrices and vectors if he has a good grounding in arithmetic. Unfortunately, though, we are not getting as good training in arithmetic as our parents and grandparents got. Among the many branches of arithmetic formerly taught was alligation, which is a simple form of linear programming. Regrettably, the subject of alligation seems to have been dropped from the arithmetic books about the turn of the twentieth century.6