ISE 222 • Midterm I • 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

Introduction

Preemptive Goal Programming

Example 1

Example 2

Constraint Slopes

Objective Function Slope

Range of Objective Function Coefficients

Shadow Price

Example

Introducing Artifical Variables

Big M Method

Example 1

Example 2

Two Phase Method

Example 3

Example 4

What is duality?

Example 1

Example 2

Example 2

Complementary Slackness

Example 4

Example 5

Algebraic Solution of LP

Example 0

Sensitivity Analysis Procedure

Changing Coefficients of a Non-Basic Variable

Example 1

Example 2

Changing Right-Hand-Side of a Constraint

Example 3

Changing Coefficients of a Basic Variable

Example 4

Example 5

Linear Programming 1

Linear Programming 2

Linear Programming 3

Linear Programming 4

Linear Programming 5

Linear Programming 6

Linear Programming 7

Graphical Solution 1

Graphical Solution 2

Graphical Solution 3

Graphical Solution 4

Simplex Method 1

Simplex Method 2

Simplex Method 3

Simplex Method 4

Simplex Method 5

Goal Programming 1

Goal Programming 2

Goal Programming 3

Graphical Sensitivity 1

Graphical Sensitivity 2

Big M Method 1

Big Method 2

Big M Method 3

Big M Method 4

Two Phase Method 1

Two Phase Method 2

Two Phase Method 3

Two Phase Method 4

Duality 1

Duality 2

Duality 3

Duality 4

Duality 5

Duality 6

Two Phase Method

Graphical Solution

Linear Programming

Goal Programming