## Integer Linear Programming – Graphical Method – Optimal Solution, Mixed, Rounding, Relaxation

Welcome to this Graphical introduction to Integer Linear programming. We will be exploring some properties of all-integer and mixed-integer linear models, and also discuss binary (or 0-1) variables in a later video. In an integer linear program, some or all… Continue Reading

## Linear Programming 5: Alternate solutions, Infeasibility, Unboundedness, & Redundancy

Welcome to this tutorial as we discuss special cases encountered while solving some linear programming problems. The special cases we’ll discuss include Alternative optimal solutions Infeasibility Unboundedness, and Redundancy. Let’s begin with alternate optimal solutions. Consider this linear programming problem… Continue Reading

## LP Graphical Method (Multiple Optimal Solutions)

Welcome. In this tutorial, I will solve this LP problem using graphical approach and use it to explain the special case of alternative or multiple optimal solutions. Let’s begin by finding points for drawing the constraint lines. For the first… Continue Reading

## Linear Programming 2: Graphical Solution – Minimization Problem

Welcome! In this tutorial, we will graphically solve this minimization problem using the Objective Function Line Approach. Note that the use of the graphical approach is limited to 2 decision variables. We start by finding points for the constraint lines.… Continue Reading