Solution of parametrized linear inequalities by fourier elimination and its applications

The parametric solution of a linear system of inequalities $Ax\leq Bb$, with parameter b, is considered. Fourier elimination is used to give a facial representation for the set of b-values for which the system is consistent. Some interesting applications of the problem are discussed. Although the worst case complexity of the method is an exponential function of the size of A, the computations are intuitive and very simple