## 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 37

Feasible region 2 FIGURE 3.5 The Wyndor Glass Co. problem would have

multiple

. 0 2 4 6 8 10 X1 on the line segment connecting ( 2,6 ) and ( 4 , 3 ) would be

Feasible region 2 FIGURE 3.5 The Wyndor Glass Co. problem would have

multiple

**optimal**solutions if the objective function were changed to Z = 3x1 + 2x2. 0 2 4 6 8 10 X1 on the line segment connecting ( 2,6 ) and ( 4 , 3 ) would be

**optimal**.Page 130

3.2 ( under the definition of

one

that every point on the line segment between ( 2 , 6 ) and ( 4 , 3 ) is

3.2 ( under the definition of

**optimal**solution ) that a problem can have more thanone

**optimal**solution . ... in the Wyndor Glass Co. problem to Z = 3x , + 2x2 , sothat every point on the line segment between ( 2 , 6 ) and ( 4 , 3 ) is

**optimal**.Page 278

With the current value of c2 = 3 , the

increased , this solution remains

becomes

4x2 = 18.

With the current value of c2 = 3 , the

**optimal**solution is ( 4 , 3 ) . When cz isincreased , this solution remains

**optimal**only for c2 4. For cz > 4 , ( 0 , 3 )becomes

**optimal**( with a tie at c2 = 4 ) , because of the constraint boundary 3xı +4x2 = 18.

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### Common terms and phrases

activity additional algorithm allocation allowable amount apply assignment basic solution basic variable BF solution bound boundary called changes coefficients column complete Consider constraint Construct corresponding cost CPF solution decision variables demand described determine distribution dual problem entering equal 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 Maximize million Minimize month needed node nonbasic variables objective function obtained operations optimal optimal solution original parameters path plant possible presented primal problem Prob procedure profit programming problem provides range remaining resource respective resulting revised shown shows side simplex method simplex tableau slack solve step supply Table tableau tion unit values weeks Wyndor Glass zero