Technical Note—Solutions of a Special Class of Linear Programming Problems

Abstract

Explicit solutions for linear problems of the form: maximize ( h , x ), subject to Ax ≦ b , b ∈ R ( A ), are given, as well as explicit solutions for its dual problem. This note replaces the full row rank assumption on A of earlier results of Ben-Israel and Charnes by the assumption b ∈ R ( A ). With this assumption, explicit solutions are derived for the dual problem that are different from related results of Zlobec and Ben-Israel.