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Lecture17aa - Lecture Examples of LP’s 2 Diet Problem –...

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Lecture 2/27/08 Examples of LP’s 2. Diet Problem Examples of Bad, Fair, and Excellent Definitions of Decision Variables. Scheduling Problem
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Diet Problem Problem #3, Page 71 in Text Nutrients and Costs per Pound Vitamin A units Vitamin C units Cost Food 1 3 1 $7 Food 2 1 1 $1 Required 12 6
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Definition of Variables Bad Definition Let x 1 =Food 1 Let x 2 =Food 2 This is probably clear to the modeler but not to the reader! Fair Definition Let x 1 =Amount of Food 1 required to meet nutritional requirements. Let x 2 =Amount of Food 2 required to meet nutritional requirements. Better but definition should include physical units and time element (if any)
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Formulation of LP Excellent variable definition Let x 1 =Amount of Food 1 required (lbs/day) to meet nutritional requirements Let x 2 =Amount of Food 2 required (lbs/day) to meet nutritional requirements. Minimize daily cost = $7x 1 +$1x 2 Constraints 3x 1 +x 2 ≥12 (Vitamin A requirement) x 1 +x 2 ≥6 (Vitamin C requirement) x 1, x 2 ≥0
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Graphical Solution to LP X 1 x 2 12 4 Vitamin A constraint 6 6 Vitamin C constraint Isocost line: $7x 1 +$1x 2 =$49
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