A Note on the Calculation of Certain Constrained Maxima

In a recent paper [1] Umland and Smith discussed the use of LaGrange multipliers in constrained response surface fitting. The technique they described is concerned with constraints in the form of equalities. In the course of computation, a set of non-linear simultaneous equations must be solved. The purpose of this note is to point out that considerable generalization is possible when the constraints are extended to inequalities. Also, it is not necessary to solve a system of simultaneous non-linear equations. By a slight modification of procedure, considerable computing labor saving can be achieved. Finally, the sufficiency criteria for solution of non-linear systems are discussed.