IE 311 • Midterm II • Operations Research I

Standard Form of LP

Example 1

Basic Solutions - Basic Feasible Solutions

Example 2

Convex Functions

Example 3 & 4

Convex Sets

Hyperplane/Half-Space/Polyhedron

Extreme Points and Directions

Example 5

Minkowski's Theorem

What is Simplex Method?

Example 1

Example 2

Example 3

Example 4 (Minimization)

Example 5 (Minimization)

Example 6 (Reverse)

Infeasible LP

Alternative Optimal Solutions

Unbounded LP

Direction of Unboundedness

Degeneracy

Introducing Artifical Variables

Big M Method

Example 1

Example 2

Two Phase Method

Example 3

Example 4

What is duality anyway?

Example 1

Example 2

Example 3

Meaning of Dual Varibles and Complementary Slackness

Example 4

Example 5

Simplex Method

Big M Method

Big M Method Example

Two Phase Method

Two Phase Method Example

Matrices of LP

Example 1

Forming a Table with Given BV

Example 2

Simplex Method in Matrix Form

Example 3

Example 4

Revised Simplex

Example 5

Example 6

Preliminaries 1

Preliminaries 2

Preliminaries 3

Preliminaries 4

Preliminaries 5

Simplex Method 1

Simplex Method 2

Simplex Method 3

Simplex Method 4

Simplex Method 5

Simplex Method 6

Simplex Method 7

Simplex Method 8

Simplex Method 9

Simplex Method 10

Simplex Method 11

Simplex Method 12

Big M Method 1

Big M Method 2

Big M Method 3

Big M Method 4

Big M Method 5

Big M Method 6

Two Phase Method 1

Two Phase Method 2

Two Phase Method 3

Two Phase Method 4

Two Phase Method 5

Duality 1

Duality 2

Duality 3

Duality 4

Duality 5

Duality 6

Duality 7

Big-M/Two-Phase/Python 1

Big-M/Two-Phase/Python 2

Big-M/Two-Phase/Python 3

Big-M/Two-Phase/Python 4

Big-M/Two-Phase/Python 5

Matrix Form 1

Matrix Form 2

Revised Simplex 1

Revised Simplex 2