The revised simplex method is one of the most efficient existent algorithms to solve linear programming problems, with applications in areas such as management, resources distribution, among others. This work has the objective of studying the simplex method, as well as to develop free code based on this method. A preliminary algorithm was implemented using Scilab software and computational tests were conducted using small instances. The efficiency of the algorithm will be improved by the addition of an LU factorization module. In further work, we intend to develop an open source application in C language, which allows the use of the simplex method through a friendly interface.