A visualization scheme as a tool to find the solution of any 3D-linear programming problem is introduced. The presented approach is highly suitable to draw and visualize interactively the feasible region of a given 3D-linear programming problem. It can be used for a better understanding of the solution process when different methods devoted to solve the underlying problem are applied, e.g., the simplex method. The proposed technique comprises sensitive analysis during the solution process and interactive visualization of the feasible region. The analysis leading to the introduced schema also shows that the design of an appropriate and simple vertex representation is crucial to manage any order of degeneracy. To deal with this paradigm and to some extent to formalize it, the concept of adjacency invariance is introduced. Several experiments have been conducted to test and assess the performance of the introduced concepts and techniques.