The Usefulness of Lagrange Multipliers in Everyday Life

Abstract

Lagrange multipliers are a very useful technique in multivariable calculus, but all too often they are poorly taught and poorly understood. With luck, this overview will help to make the concept and its applications a bit clearer.One of the most common problems in calculus is that of finding maxima or minima (in general, “extrema”) of function, but it is often difficult to find a closed form for the function being extremized. Such difficulties often arise when one wishes to maximize or minimize a function subject to fixed outside conditions or constraints. The method of Lagrange multipliers is a powerful tool for solving this class of problems without the need to explicitly solve the conditions and use them to eliminate extra variables.