On Lagrange Multipliers in Work with Quality and Reliability Assurance

In optimizing some property of a system, reliability say, a designer usually has to accept certain constraints regarding cost, completion time, volume, weight, etc. The solution of optimization problems with boundary constraints can be helped substantially by the use of Lagrange multipliers techniques (LMT). With representative examples of increasing complexity, the wide applicability of LMT is illustrated. Two particular features are put in focus. First, an easy to follow yet powerful new graphical approach is presented, Second, the concept of Fuller-Polya maps is shown to be helpful in the areas of sales promotion and teaching. These maps illuminate the logic structure of solution sequences. One such map is shown, illustrating the application of LMT in one of the examples.