## Elementary Linear Programming with ApplicationsLinear programming finds the least expensive way to meet given needs with available resources. Its results are used in every area of engineering and commerce: agriculture, oil refining, banking, and air transport. Authors Kolman and Beck present the basic notions of linear programming and illustrate how they are used to solve important common problems. The software on the included disk leads students step-by-step through the calculations. The Second Edition is completely revised and provides additional review material on linear algebra as well as complete coverage of elementary linear programming. Other topics covered include: the Duality Theorem; transportation problems; the assignment problem; and the maximal flow problem. New figures and exercises are provided and the authors have updated all computer 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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0-ratios artificial variables augmented matrix basic feasible solution basic solution branch and bound canonical form closed half-space coefficients Consider the linear constraints convex set CTX subject cutting plane delay point departing variable directed arc dual problem dual simplex method dual variables entering variable equation Example extreme point final tableau graph inequality initial basic feasible initial tableau input integer programming problem linear programming problem linear system linearly independent maximal flow Maximize z minimization problem mixed integer programming negative entries node nonbasic variables nonnegative objective function objective function value objective row obtain Tableau optimal solution optimality criterion path pivotal column pivotal row primal problem problem in canonical profit programming problem Maximize represents route row echelon form row equivalent satisfies Section 1.1 set of feasible simplex algorithm slack variables solve standard form Step subject to Ax supersource Suppose transportation problem vector zero