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 237
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 , x1 = 0 , x2 = 6 , and X2 Y1 = 0 , y2 = 2 , y3 = 0 , with cx = 30 = yb .
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 , x1 = 0 , x2 = 6 , and X2 Y1 = 0 , y2 = 2 , y3 = 0 , with cx = 30 = yb .
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 287
( b ) At each iteration , the simplex method simultaneously identi- fies 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 ...
( b ) At each iteration , the simplex method simultaneously identi- fies 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 ...
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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
Bibliographic information
| Title | Introduction to Operations Research McGraw-Hill International Editions McGraw-Hill industrial & plant engineering series McGraw-Hill series in industrial engineering and management science |
| Authors | Frederick S. Hillier, Gerald J. Lieberman |
| Edition | 7, illustrated |
| Publisher | McGraw-Hill, 2001 |
| Original from | Pennsylvania State University |
| Digitized | 26 Aug 2009 |
| ISBN | 0071181636, 9780071181631 |
| Length | 1214 pages |
| Export Citation | BiBTeX EndNote RefMan |