LP_model_graphical_solution

LP_model_graphical_solution - LP—Graphical Solution...

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Unformatted text preview: LP—Graphical Solution Method MSci331—Week 2 Click to edit Master subtitle style 9/13/11 Convex Set and Extreme Points 9/13/11 LP: Example (Papa Louis ) • Papa Louis manufacturers wooden tables and chairs for small kids. Each "table" built: Sells for $27 and uses $10 worth of raw materials, increases Papa Louis’s variable labor/overhead costs by $14. Requires 2 hours of finishing labor and 1 hour of carpentry labor. Each "chair" built: Sells for $21 and uses $9 worth of raw materials, increase Papa Louis’s 9/13/11 LP: Example (Papa Louis ) 9/13/11 LP: Example (Papa Louis ) 9/13/11 LP: Example (Papa Louis ) 9/13/11 LP: Example (Papa Louis ) 9/13/11 Example: 2 Max s.t. 371BP100 + 461BP200 8BP100 5BP100 2BP100 -0.25BP100 + + + + 12BP200 10BP200 2BP200 0.75BP200 ≤ ≤ ≤ ≥ 600 450 140 0 Machining and Welding Painting and Finishing Assembly, Test, and Packaging BodyPlus 200 Requirement BP 100, BP 200 > 0 9/13/11 88 Example 2: Multiple Optimal Solutions • Consider the LP model 9/13/11 Example 2: Multiple Optimal Solutions 9/13/11 Infeasible Solution 9/13/11 Unbounded Solution 9/13/11 LP Model to Standard Form • Convert LP format to a standard form 9/13/11 Insight from the Geometric Procedure For a constraint to be reasonable, all terms in the constraints must have the same units. 9/13/11 Insights from the Geometric Procedure x2 1 (x1=0,x2=0,Z=0) 2 (x1=0,x2=5,Z=15) 40 8 (x1=5,x2=10,Z=40) 35 1 0 7 (x1=20,x2=5,Z=55) 9 30 Constraint 1 25 Constraint 3 20 Z 8 15 3 2 10 9/13/11 1 Constraint 2 1 0 5 5 (x1=20,x2=0,Z=40) 0 5 10 15 20 7 6 25 30 35 40 x 1 Basic and Nonbasic Variables x2 40 Max Z = 2 x1 + 3x2 35 30 9 25 Constraint 1 20 Constraint 3 15 Z 8 3 10 9/13/11 2 5 10 5 Constraint 2 6 1 0 5 10 10 15 20 7 25 30 35 40 x1 ...
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This note was uploaded on 09/12/2011 for the course MSCI 311 taught by Professor Dumeiring during the Fall '09 term at Waterloo.

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LP_model_graphical_solution - LP—Graphical Solution...

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