IE 3033 • Midterm I + II • Operations Research I

What is Linear Programming?

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

Example 9

Example 10

Solving LP with 2 variables

Example 1

Example 2

Example 3

Alternative Optimal Solutions

Example 4

Standard Form of LP

Example 1

Basic Solutions - Basic Feasible Solutions

Example 2

What is Simplex Method?

Example 3

Example 4

Example 5

Example 6 (Minimization)

Example 7 (Minimization)

Example 8 (Reverse)

Infeasible LP

Alternative Optimal Solutions

Unbounded LP

Degeneracy

Introducing Artifical Variables

Big M Method

Example 1

Example 2

Two Phase Method

Example 3

Example 4

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

Standard Form of LP (Tekrar)

Basic Solutions / Basic Feasible Solutions (Tekrar)

Convex Functions

Examples

Convex Sets

Hyperplane/Half-Space/Polyhedron

Extreme Points and Directions

Example

Minkowski's Theorem

Formulation of Linear Programming Models 1

Formulation of Linear Programming Models 2

Formulation of Linear Programming Models 3

Formulation of Linear Programming Models 4

Formulation of Linear Programming Models 5

Formulation of Linear Programming Models 6

Formulation of Linear Programming Models 7

Graphical LP Solution 1

Graphical LP Solution 2

Simplex Method 1

Simplex Method 2

Simplex Method 3

Simplex Method 4

Simplex Method 5

Simplex Method 6

Big M Method 1

Big M Method 2

Two Phase Method 1

Two Phase Method 2

Matrix Form 1

Matrix Form 2

Revised Simplex 1

Revised Simplex 2

Simplex Method Fundamentals 1

Simplex Method Fundamentals 2

Simplex Method Fundamentals 3