## Overview of Week 8

• #### 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: Sensitivity Analysis
• What is the fundamental block matrix product that shows how every simplex tableau can be obtained by multiplying the initial tableau on the left by a nonsingular matrix?
• tableau approach to sensitivity analysis (block matrix structure)
• break-even price
• reduced cost
• marginal values
• objective coefficient range
• right hand side (or resource) range
• pricing out
• the fundamental theorem on sensitivity analysis
• #### Key Concepts:

• Section 4:
• The Strong Duality Theorem
• Complementary slackness
• general duality correspondences
• primal and dual feasibility for tableaus and dictionaries
• the dual simplex algorithm
• Section 5:
• vertices and basic feasible solutions
• geometry of duality
• geometry of degeneracy
• Section 6:
• What is the fundamental block matrix product that shows how every simplex tableau can be obtained by multiplying the initial tableau on the left by a nonsingular matrix?
• tableau approach to sensitivity analysis (block matrix structure)
• break-even price
• reduced cost
• marginal values
• objective coefficient range
• right hand side (or resource) range
• pricing out
• the fundamental theorem on sensitivity analysis
• #### Skills to Master:

• setting up the auxiliary problem and applying the initial pivot
• applying the two phase simplex algorithm
• computing general duals without conversion to standard form
• Apply the dual simplex algorithm
• apply the Geometric Duality Theorem to assess optimality
• #### Quiz:

Friday, November 15.
• The first question on the quiz will concern the theory and vocabulary words from Sections 5 and 6. In the second question you will be asked to apply the Geometric Duality Theorem to assess optimality.