Programação linear: problema de transportes aplicado no ensino médio.

Abstract

This paper aims to propose a methodology to approach High School on the Linear Programming focusing on optimization (maximization or minimization) through mathematical modeling and the Transportation Problem. The subjects needed to understand it are similar function, first degree inequalities, matrices, determinants and linear systems, which are addressed in the first and second year of High School. The introduction presents a brief study of the history of Operational Research to understand the historical and geopolitical context of the period of its creation, thus demonstrating its importance and evolution over the years. Then its main application tool, the Linear Programming, is presented, and the two-variables problem solving methods (graphical method) are studied, and can be presented in the first year of high school; and for the resolution of two or more variables, there is a special type of Linear Programming known as the Simplex Method, which can be presented in the second year of High School. In order to condense knowledge and give real applicability to the taught content, Transportation Problem is presented, wich is simply a special type of Simplex method, with the aim of determining the loading of a transportation network that connects various sources to various destinations, so that the total cost of transportation is minimal. Due to the large number of variables that can be obtained in na optimization problem, Geogebra and Microsoft Excel (Solver) software are used to facilitate the visualization and resolution of the problems.