The teaching experience of the revised simplex method in matrix notation on the blackboard leads us to prepare a visualization alternative, useful for the constituting part of the education liturgy. According to our approach the educator does not spend anymore valuable time on boring calculations while the student understands complex mathematical concepts. Our courseware has unique features like: actual solution to the simplex problem, on screen animation and intervention points. The program is a Java application, running through any browser and evaluated at University of Macedonia at Thessaloniki.