## Introduction to Operations Research, Volume 1-- This classic, field-defining text is the market leader in Operations Research -- and it's now updated and expanded to keep professionals a step ahead -- Features 25 new detailed, hands-on case studies added to the end of problem sections -- plus an expanded look at project planning and control with PERT/CPM -- A new, software-packed CD-ROM contains Excel files for examples in related chapters, numerous Excel templates, plus LINDO and LINGO files, along with MPL/CPLEX Software and MPL/CPLEX files, each showing worked-out examples |

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Page 237

If x is not optimal for the

If x is not optimal for the

**primal problem**, then y is not feasible for the dual problem . To illustrate , after one iteration for the Wyndor Glass Co. problem , xy = 0 , x2 = 6 , and yı = 0 , y2 = { , yz = 0 , with cx = 30 = yb .Page 286

( b ) Use duality theory to show that the optimal solution for the

( b ) Use duality theory to show that the optimal solution for the

**primal problem**has Z < 0 . 6.1-6 . Consider the following problem . Maximize Z = 2x1 + 6x2 + 9x3 , subject to X1 + x3 = 3 x2 + 2x3 = 5 ( resource 1 ) ( resource 2 ) and ...Page 287

( b ) At each iteration , the simplex method simultaneously identifies a CPF solution for the

( b ) At each iteration , the simplex method simultaneously identifies a CPF solution for the

**primal problem**and a CPF solution for the dual problem such that their objective function values are the same . ( c ) If the**primal problem**...### What people are saying - Write a review

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### Common terms and phrases

activity additional algorithm allowable amount apply assignment basic solution basic variable BF solution bound boundary called changes coefficients column complete Consider constraints Construct corresponding cost CPF solution decision variables demand described determine distribution dual problem entering equal equations estimates example feasible feasible region FIGURE final flow formulation functional constraints given gives goal identify illustrate increase indicates initial iteration linear programming Maximize million Minimize month needed node nonbasic variables objective function obtained operations optimal optimal solution original parameters path Plant possible presented primal problem Prob procedure profit programming problem provides range remaining resource respective resulting shown shows side simplex method simplex tableau slack solve step supply Table tableau tion unit weeks Wyndor Glass zero