Simplex Method

1
Simplex Method

• Terms you should know from chapter 2 (Chvatal)
• Dictionary
• Feasible dictionary
• Slack variables
• Decision variables
• Basic solutions
• Basic variables
• Nonbasic variables
• Basis
• Pivoting

2
Problem 2.1 (a) on page 26

• Write down initial dictionary, entering variable
  (using rule of max coeff), leaving variable
• Write down second dictionary, same info
• Etc. until you have a final dictionary

3
Problem 2.1 (c) on page 26

• Do same for problem 2.1 (c)
• Also draw original constraints geometrically in
  plane (x-axis x1, y-axis x2)
• What conclusion can you draw from this geometric
  drawing

4
Question

• Given a system with n variables (before
  introduction of slack variables) and m
  inequalities (not including xi 0), how many
  basic solutions are there?
• What does this imply about the worst-case running
  time of simplex method?