Mathematical Model of the Criterion of Optimization by Compensation for Designing Commercial Bottles with Lateral Surfaces of Revolution and a Straight Section along Its Silhouette

In this article, the mathematical foundations of the so called Criterion of Optimization by Compensation for designing commercial bottles with a straight section along its silhouette and with lateral surfaces of revolution is presented. Such mathematical model uses as main tools, Lagrange polynomial interpolation and Newton’s Method for Nonlinear Systems being first necessary to formulate and demonstrate a theorem. It was redesigned and manufactured a bottle of a half-liter of Fanta soda of the well-known Coca Cola Company, which uses 18.86% more material that such criterion establishes. It was expected that the redesigned bottle use 4.91% more of material with respect to what is established by the Criterion of Optimization by Compensation. However, it was reported a 13% of mistake due to important limitations that must be overcome.