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
... problem . Maximize Z = x1 + 2x2 , subject to -x1 + x2 ≤ 2 4x1 + x2 ≤ 4 x ; ≥ 0 , for j = 1 , 2 , 3 , 4 , 5 . and ... dual problem . ( b ) Use duality theory to show that the optimal solution for the primal problem has Z ≤ 0 ...
... problem . Maximize Z = x1 + 2x2 , subject to -x1 + x2 ≤ 2 4x1 + x2 ≤ 4 x ; ≥ 0 , for j = 1 , 2 , 3 , 4 , 5 . and ... dual problem . ( b ) Use duality theory to show that the optimal solution for the primal problem has Z ≤ 0 ...
Page 288
Frederick S. Hillier, Gerald J. Lieberman. sic solution for the dual problem by using Eq . ( 0 ) for the pri- mal problem . Then draw your conclusions about whether these two basic solutions are optimal for their respective problems . 1 ...
Frederick S. Hillier, Gerald J. Lieberman. sic solution for the dual problem by using Eq . ( 0 ) for the pri- mal problem . Then draw your conclusions about whether these two basic solutions are optimal for their respective problems . 1 ...
Page 289
... 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 . 6.4-5 . Consider the two versions of the dual problem ...
... 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 . 6.4-5 . Consider the two versions of the dual problem ...
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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 dual problem dual simplex method dynamic programming entering basic variable estimates example feasible region feasible solutions final simplex tableau final tableau following problem formulation functional constraints Gaussian elimination given goal programming 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 slack variables solve the model Solver spreadsheet step subproblem surplus variables Table tion unit profit values weeks Wyndor Glass x₁ zero