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CPSC 335

Linear ProgrammingLinear Programming

Dr. Marina Gavrilova

Computer Science

University of Calgary

Canada

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Linear Programming

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Political Campaign Example

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Political Campaign Example

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Political Campaign Example

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Political Campaign Example

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Political Campaign Example

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Solution ??

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Manufacturing Example

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Manufacturing Example

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Manufacturing Example

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Manufacturing Example

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General Form of LP

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General Form of LP

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General Form of LP

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Canonical Forms for Linear Programs

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2D Geographical Explanation of Simplex

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Graphical View of Simplex

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Applying Objective Function

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Slack Form

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Standard to Slack Form

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Dual of LP

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General Form

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General Rules for Constructing Dual

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General Rules for Constructing Dual

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General Rules for Constructing Dual

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Applications of Linear Programming

Web links: http://www.rpi.edu/~mitchj/handouts/lp/lp.pdf http://www.thehindubusinessline.com/mentor/2005/12/26/stories/

2005122601681000.htm http://www.tki.org.nz/r/asttle/pdf/technical-reports/techreport05.pdf

Many practical problems in operations research can be expressed as linear programming problems. Examples:

- network flow - duality - decomposition - convexity