The multiparametric linear programming (MLP) problem for the right-hand sides (RHS) is to maximize z = c<sup>T</sup>x subject to Ax = b(\lambda), x \geqq 0, where b(\lambda) be expressed in the form <disp-formula><tex-math><![CDATA[$$ b(\lambda) = b^\ast + F \lambda, $$]]></tex-math></disp-formula> where F is a matrix of constant coefficients, and \lambda is a vector-parameter. The multiparametric linear programming (MLP) problem for the prices or objective function coefficients (OFC) is to maximize z = c<sup>T</sup>(v)x subject to Ax = b, x \geqq 0, where c(I) can be expressed in the form c(v) = c* + Hv, and where H is a matrix of constant coefficients, and v a vector-parameter. Let B<sub>i</sub> be an optimal basis to the MLP-RHS problem and R<sub>i</sub> be a region assigned to B<sub>i</sub> such that for all \lambda \epsilon R<sub>i</sub> the basis B<sub>i</sub> is optimal. Let K denote a region such that K = U<sub>i</sub>R<sub>i</sub> provided that the R<sub>i</sub> for various I do not overlap. The purpose of this paper is to present an effective method for finding all regions R<sub>i</sub> that cover K and do not overlap. This method uses an algorithm that finds all nodes of a finite connected graph. This method uses an algorithm that finds all nodes of a finite connected graph. An analogus method is presented for the MLP-OFC problem.
