It is shown how extremal principles may be used in their rigorous sense to solve certain optimizing problems involving inequalities. The method applies to both linear and non-linear type problems as illustrated by the examples included in the paper, and is particularly suited for electronic digital computation because of the trigger-type, “either-or,” nature of the solution. Certain problems concerned with the low weight design of structures, arising in the author's field of structural mechanics, can be considered to lie in the general field of operations research. Almost invariably these problems contain inequality side conditions and hence may be solved by the methods of the paper. Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.