## 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 155

Because the constraint on

Because the constraint on

**resource**1 , xı 5 4 , is not binding on the optimal solution ( 2 , 6 ) , there is a ... the constraints on**resources**2 and 3 , 2x2 = 12 and 3x1 + 2x2 = 18 , are binding constraints ( constraints that hold with ...Page 181

( b ) Use graphical analysis to find the shadow prices for the

( b ) Use graphical analysis to find the shadow prices for the

**resources**. ( c ) Determine how many additional units of**resource**1 would be needed to increase the optimal value of Z by 15 . 4.7-5 . Consider the following problem .Page 241

2 9 erates at a strictly positive level ( x ; > 0 ) , the marginal value of the

2 9 erates at a strictly positive level ( x ; > 0 ) , the marginal value of the

**resources**it consumes must equal ( as ... The second statement implies that the marginal value of**resource**i is zero ( y ; = 0 ) whenever the supply of this ...### What people are saying - Write a review

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### Other editions - View all

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