Some applications of nonnegative linear systems: Farkas strikes again

This paper presents a unifying perspective for analyzing certain systems of linear equations in nonnegative variables that arise in diverse areas of operations research economic exchange models, finite Markov chains, directed graphs, and zero-one quadratic programs. Karkas’ lemma is seen to play a central role in establishing general existence, uniqueness, and positivity results. A new application involving Lagrangian duality is developed.