Lagrange Multipliers to Optimize Functions of Several Variables

We examine and demonstrate the Method of Lagrange Multipliers in Optimization of functions of several variables. This project covers optional material supplementing a Calculus III course. In this project we will discuss the need for the method and demonstrate a proof of the method. We then apply the method in an application from business demonstrating its usefulness by comparing solutions with and without the use of Lagrange Multipliers. We conclude with an application showing the geometric mean of a list of numbers is always less than or equal to the arithmetic mean of the same list of numbers. A comparison of the geometric mean and arithmetic mean of two consecutive whole numbers is relevant to the apportionment of the House of Representatives