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Chapter 2 g
An Introduction to Linear Programming
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LearninggObjectives
1. Obtaingangoverviewgofgthegkindsgofgproblemsglineargprogrammingghasgbeengusedgtogsolve.
2. Learnghowgtogdevelopglineargprogramminggmodelsgforgsimplegproblems.
3. Begablegtogidentifygthegspecialgfeaturesgofgagmodelgthatgmakegitgaglineargprogramminggmodel.
4. Learnghowgtogsolvegtwogvariableglineargprogramminggmodelsgbygtheggraphicalgsolutiongprocedure.
5. Understandgthegimportancegofgextremegpointsgingobtaininggthegoptimalgsolution.
6. Knowgthegusegandginterpretationgofgslackgandgsurplusgvariables.
7. Begablegtoginterpretgthegcomputergsolutiongofgaglineargprogramminggproblem.
8. Understandghowgalternativegoptimalgsolutions,ginfeasibilitygandgunboundednessgcangoccurginglinear
gprogramminggproblems.
9. Understandgthegfollowinggterms:
problemgformulation feasiblegregion
constraintgfunction slackgvariable
objectivegfunction standardgform
solution redundantgconstraint
optimalgsolution extremegpoint
nonnegativitygconstraints surplusgvariable
mathematicalgmodel alternativegoptimalgsolutions
lineargprogram infeasibility
lineargfunctions unbounded
feasiblegsolution
2g-g1
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1. a,gb,gandge,garegacceptableglineargprogramminggrelationships.
c isgnotgacceptablegbecausegofg −2B2
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erms.
2. a.
B
8
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0 4 8
b.
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c.
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3. a.
B
(0,9)
A
0 (6,0)
b.
B
(0,60)
A
0 (40,0)
c.
B
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onglinegaregonlygfeasibl
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(0,20)
A
0 (40,0)
4. a.
B
(20,0)
A
(0,-15)
2g-g3
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