Overview of Week 10
Math 407 Section A, November 26, 2012
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Reading Assignment:
- Course notes:Section 6: pages 1-5:
Due Friday, Nov 16.
- Course notes:Section 6: pages 5-11:
Due Monday, Nov 19.
- Course notes:Section 6: pages 11-13:
Due Wednesday, Nov 21.
- Course notes:Section 6: pages 13-14:
Due Monday, Nov 26.
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Homework Assignment:
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Vocabulary List:
- Section 5:
- hyperplane
- halfspace
- convex set
- polyhedral convex set
- vertex of a polyhedral convex set
- geometric interpretation of Basic Feasible Solutions
- geometric interpretation of Degeneracy
- geometric interpretation of Duality
- Fundamental representation theorem for vertices.
- The geometry of degeneracy.
- the relationship between primal (dual) degeneracy and
multiple optimal solutions to the (dual) primal problem.
- The Geometric Duality Theorem.
- Section 6:
- The block structured matrix interpretation of simplex pivoting
- tableau approach to sensitivity analysis (block matrix structure)
- break-even price
- reduced cost
- marginal values
- shadow prices
- objective coefficient range
- right hand side (or resource) range
- pricing out
- the fundamental theorem on sensitivity analysis
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Key Concepts:
- Section 5:
- vertices and BFSs
- geometry of duality
- geometry of degeneracy
- degeneracy and multiple optimal solutions
- Section 6:
- The block structured matrix interpretation of simplex pivoting
- tableau approach to sensitivity analysis
- Range analysis (cost coefficients and right hand sides)
- Pricing out
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Skills to Master:
- Apply the dual simplex algorithm
- computing break-even prices
- computing ranges (cost coefficients and right-hand sides)
- pricing out a new activity
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Quiz:
Friday, November 30
- The first question will either be a vocabulary word from Section 6 or one of the
models 1-28. The second question wil be a sensitivity analysis question
involving range analysis tools as well as pricing out.