COMMENT

The problem of determining where a function of several variables assumes its maximum or minimum value is obviously an important one in all branches of science. The problems that we solved in this appendix are the basic kind of such problems. From these it is possible to branch out in many directions. There are many theoretical problems, for example, in economic theory and engineering as well as in many science situations in which there are several functions of several variables with functional relations and restrictions imposed on them, and the problem is to maximize one of those functions subject to the restrictions. This is similar to the problem of linear programming, only here the functions are not linear.

The reader of this volume should be aware that a larger share of the applications of statistics and probability are concerned with how to maximize or minimize some function with some significant confidence. This obviously is a motivating force in calculus, but it is also the rationale for linear programming. Mathematical methods are certainly a powerful tool for solving this type of problem and would merit study for this reason only.