## Introduction to Operations ResearchCD-ROM contains: Student version of MPL Modeling System and its solver CPLEX -- MPL tutorial -- Examples from the text modeled in MPL -- Examples from the text modeled in LINGO/LINDO -- Tutorial software -- Excel add-ins: TreePlan, SensIt, RiskSim, and Premium Solver -- Excel spreadsheet formulations and templates. |

### From inside the book

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**primal problem**, then y is not feasible for the dual problem . To illustrate , after one iteration for the Wyndor Glass Co. problem , x1 = 0 , x2 = 6 , and X2 Y1 = 0 , y2 = 2 , y3 = 0 , with cx = 30 = yb . This x is feasible for the primal ...Page 286

... problem . Maximize Z = - -X1 - 2x2 - X3 , subject to and x1 + x2 + 2x3 ≤ 12 - X1 X2 X3 ≤ 1 X2 ≥ 0 , xz ≥ 0 . ( a ) Construct the dual problem . ( b ) Use duality theory to show that the optimal solution for the

... problem . Maximize Z = - -X1 - 2x2 - X3 , subject to and x1 + x2 + 2x3 ≤ 12 - X1 X2 X3 ≤ 1 X2 ≥ 0 , xz ≥ 0 . ( a ) Construct the dual problem . ( b ) Use duality theory to show that the optimal solution for the

**primal problem**has Z ...Page 287

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**primal problem**in column 1 , the corresponding sets of as- sociated variables for the dual problem in column 2 , and the set of nonbasic variables for each complementary basic solution in the ... problem by using Eq . CHAPTER 6 PROBLEMS 287.### Other editions - View all

Introduction to Operations Research Frederick S. Hillier,Gerald J. Lieberman No preview available - 2001 |

### Common terms and phrases

activity algebraic algorithm allowable range artificial variables b₂ basic solution c₁ c₂ changes coefficients column Consider the following cost Courseware CPLEX decision variables described dual problem dynamic programming entering basic variable estimates example feasible region feasible solutions final simplex tableau final tableau flow following problem formulation functional constraints Gaussian elimination given graphical identify increase initial BF solution integer iteration leaving basic variable linear programming model linear programming problem LINGO LP relaxation lution Maximize Z maximum flow problem Minimize needed node nonbasic variables nonnegativity constraints objective function obtained optimal solution optimality test parameters path plant presented in Sec primal problem Prob procedure range to stay resource right-hand sides sensitivity analysis shadow prices shown simplex method slack variables solve the model Solver spreadsheet step subproblem surplus variables Table tion unit profit values weeks Wyndor Glass x₁ zero