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The General LinearProgramming Problem
The Revised Simplex Method
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Aalk applications artificial vector assume basic feasible solution Calif Chap Charnes column vector computational procedure constraints convex combination convex function convex set corresponding cost coefficients defined determine developed discussion dual problem elements elimination equal to zero equations example Exercise extremal problem extreme point extreme-point solution formulation given Hence inequalities integer inverse iterations linear linear-programming problem linearly independent Management Science mathematical maximize Minimize minimum feasible solution minimum solution napkins node nonbasic variables nonlinear Nonlinear Programming nonnegative variables objective function obtain Operations Research optimal optimum solution parametric positive production programming problem RAND Corporation RAND Report reader revised simplex method row vector satisfy simplex algorithm simplex method simplex procedure simplex tableau slack variables Step subproblem subtracting techniques theorem transformation transportation problem X'CX yields