## Introduction to Linear Programming: With Applications |

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algebra artificial vectors augmented matrix basic feasible solution basic solution Basis Obj basis vectors branch change of basis coefficients column vector consider constraints convex combination convex set corresponding cost defined Definition denote determine dual problem enter the basis equations Example Exercise feasible function finite number following tableau form a basis Formulate Hence inequality integers inventory line segment linear combination linear programming problem linearly independent maximal flow maximizing problem maximum value minimizing minimum nodes nonbasis vector nonnegative number of units objective function obtain optimal basic feasible optimal solution path period proper sign prove real numbers related standard problem requirements row transformations satisfies scalar multiplication set of vectors sign for improvement signals per second simplex method simplex sequence solution of P0 solve Suppose terminal transportation problem transshipment problem unit vectors vector space xu x2