A Simple Visual Solution of the Technique of Undetermined Multipliers

Extract

For many practical purposes, Lagrange’s undetermined multipliers can be used for the solution of problems where some function has to be maximised subject to a constraint.

The technique described here arose from a consideration of one such case, where there was a choice of several types of investment, and, within each type, a different scale or level. With a limited total budget, it was necessary to decide how much to spend on each alternative.