Elementary Linear Programming with Applications
The disk that comes with the book contains the student-oriented linear programming code SMPX, written by Professor Evar Nering of Arizona State University. The authors also recommend inexpensive linear programming software for personal computers. * More review material on linear algebra* Elementary linear programming covered more efficiently* Presentation improved, especially for the duality theorem, transportation problems, the assignment problem, and the maximal flow problem* New figures and exercises* Computer applications updated* Added disk with the student-oriented linear programming code SMPX, written by Professor Evar Nering of Arizona State University* New guide to inexpensive linear programming software for personal computers
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INTRODUCTION TO LINEAR PROGRAMMING
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_ I _ artiﬁcial variables augmented matrix basic feasible solution basic solution canonical form coefﬁcient Consider the linear constraints convex set cutting plane deﬁned deﬁnition Definltiion delay point departing variable dual problem dual variables entering variable equation EXAMPLE Exercises extreme point Figure ﬁnal tableau ﬁnd ﬁnding ﬁnite ﬁrst row initial basic feasible initial tableau integer programming problem labeled linear programming problem linear system linearly independent mathematical model minimization problem mixed integer programming negative entries node nonbasic variables nonnegative objective function objective row Operations Research optimal solution path pivotal column primal problem proﬁt programming problem Maximize real number reduced row echelon represents route row echelon form satisﬁes Section 2.1 simplex algorithm simplex method slack variable solve speciﬁed standard form Step subject to 2x subspace supersource Suppose Theorem transportation problem zero