The objective of this work is to develop a computational application for the implementation of the simplex algorithm using two-phase method and the Lower-Upper decomposition. Since companies have applied linear models with excellent results, the simplex algorithm is a mandatory topic in undergraduate and graduate programs in engineering and business. However, the available literature to teach it introduces the tableau method that is the least efficient for its computational implementation. To solve this problem, we programmed a computational application in Visual Basic with three modules: Declarations, Outputs/Inputs, and Procedure. To solve a problem, the user enters it in its standard form and performs the iterations by clicking on the button indicated in the application. By using our application in the classroom, students get better grades in the evaluation of this part of the course. We can conclude that student understand and can develop the algorithm and not only obtain the solution as done with commercial software.