Introduction to Operations Research, Volume 1CD-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
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 ...
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 ) 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 .
( 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 .
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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 allocation allowable range artificial variables assignment problem augmenting path basic solution Big M method changes coefficients column Consider the following constraint boundary corresponding CPLEX decision variables dual problem dynamic programming entering basic variable example feasible region feasible solutions final simplex tableau final tableau following problem formulation functional constraints Gaussian elimination given goal goal programming graphically identify increase initial BF solution integer interior-point iteration leaving basic variable linear programming model linear programming problem LP relaxation lution Maximize Maximize Z maximum flow problem Minimize needed node nonbasic variables objective function obtained optimal solution optimality test path Plant presented in Sec primal problem Prob procedure range to stay resource right-hand sides sensitivity analysis shadow prices slack variables solve this model Solver spreadsheet step subproblem surplus variables tion transportation problem transportation simplex method weeks Wyndor Glass x₁ zero
Bibliographic information
| Title | Introduction to Operations Research, Volume 1 Introduction to Operations Research, Frederick S. Hillier 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 | the University of Michigan |
| Digitized | 8 Aug 2011 |
| ISBN | 0072321695, 9780072321692 |
| Length | 1214 pages |
| Export Citation | BiBTeX EndNote RefMan |