## 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 286

( a )

( a )

**Construct**the dual problem . ( 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 ...Page 288

6.1-4b . subject to ( a )

6.1-4b . subject to ( a )

**Construct**its dual problem . xy + 2x2 10 ( b ) Solve this dual problem graphically . 2x1 + x2 > 2 ( c ) Use the result from part ( b ) to identify the nonbasic variables and and basic variables for the optimal ...Page 289

( a )

( a )

**Construct**the dual problem . ( b ) Use graphical analysis of the dual problem to determine whether the primal problem has feasible solutions and , if so , whether its objective function is bounded .### What people are saying - Write a review

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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