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. |
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Page 286
( 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 . Z = 2x1 + 6x2 + 9x3 , Maximize subject to X1 + x3≤3 x2 + 2x3 ≤5 ...
( 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 . Z = 2x1 + 6x2 + 9x3 , Maximize subject to X1 + x3≤3 x2 + 2x3 ≤5 ...
Page 288
( a ) Construct its dual problem . ... elimination to solve for its basic variables , starting from the initial system of equations [ excluding Eq . ( 0 ) ] constructed for the simplex method and setting the nonbasic variables to zero .
( a ) Construct its dual problem . ... elimination to solve for its basic variables , starting from the initial system of equations [ excluding Eq . ( 0 ) ] constructed for the simplex method and setting the nonbasic variables to zero .
Page 289
For each of the following linear programming models , use the SOB method to construct its dual problem . ... then constructing its dual problem , and next con- verting this dual problem to the form obtained in part ( a ) . 6.4-8 .
For each of the following linear programming models , use the SOB method to construct its dual problem . ... then constructing its dual problem , and next con- verting this dual problem to the form obtained in part ( a ) . 6.4-8 .
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Introduction to Operations Research Frederick S. Hillier,Gerald J. Lieberman No preview available - 2001 |
Common terms and phrases
activity additional algorithm allowable amount apply assigned basic solution basic variable BF solution bound boundary called changes coefficients column complete Consider Construct corresponding cost CPF solution decision variables described determine developed dual problem entering equations estimates example feasible feasible region feasible solutions FIGURE final flow formulation functional constraints given gives goal identify illustrate increase indicates initial iteration linear programming linear programming model Maximize million Minimize month needed node objective function obtained operations optimal optimal solution original parameters path perform plant possible presented primal problem Prob procedure profit programming problem provides range resource respective resulting revised sensitivity analysis shown shows side simplex method simplex tableau slack solve step Table tableau tion unit values weeks Wyndor Glass x₁ zero