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.

Homework Assignment:

• Supplemantary Exercises:
  • Sensitivity: Silicon Chip Corporation: Due Monday, Nov 26.
  • Sensitivity: Concrete Products Corporation: Due Wednesday, Nov 28.
  • Sensitivity: Concrete Products Corporation: Due Friday, Dec. 1.
  • Sensitivity: The Family Farm: Due Monday, Dec. 3.
  • Modeling: Modeling problems 1-25 on the class webpage. Due Monday, November 26.
  • Modeling: Modeling problems 1-28 on the class webpage. Due Friday, November 30.

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

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

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

Quiz: