Sets of feasible solutions.

In this lesson we discuss how the algebraic structure of the set of all solutions of the systems of linear equations and inequalities is. We start by linear systems of equations homogeneous and complete, and continue with the case of inequalities, which is the most interesting. We show that the most general solution of a complete linear system of inequalities is the sum of a linear space plus a cone plus a polytope. To illustrate the different cases we give some examples. Finally, we use the knowledge of this general solution to obtain very easily all the solutions of LPP and use a truncated cube example for illustration purposes.";