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Definitions and Fundamental Properties
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additional equation algebraic applied arbitrary artificial variables associated augmented problem basic solution basic variables calculations capacity Chapter coefficients column column-vectors components constraints convex convex combination convex cone convex set corresponding D. R. Fulkerson defined dual algorithm dual problem dual program equal example exists extremal point extremal program feasible finite number Ford-Fulkerson Ford-Fulkerson algorithm given graph hyperplane inequalities initial program integer program inverse L. R. Ford labelled lexicographic linear programming linearly independent matrix maximal flow minimal Moreover negative nodes non-negative non-zero number of iterations obtained optimal basis optimal program original problem preceding Proof replaced restricted primal satisfied secondary variables Section set of indices simplex algorithm simplex method simplex tableau slack variables square standard form submatrix supporting hyperplane suppose theorem transformation transportation problem variable xj vector zero