Part 3: The Algorithm Under the Hood
Are you ready to dive into the inner workings of linear programming? In this article, we will explore the fascinating world of the simplex method, the algorithm commonly used to solve linear programming problems. Get ready to unravel the complexity and beauty of this mathematical tool as we delve into its intricacies and explore its practical applications.
Up until now, this series has covered the basics of linear programming. In this article, we are going to move from basic concepts into the details under the hood! This article will cover the simplex method, which is the algorithm that is often used to solve linear programming problems. While we will solve a simple linear programming example by hand with the simplex method, our focus will be on the intuition of the algorithm rather than memorizing the algorithmic steps (we have computers for that kind of stuff!).
Here is what we will cover:
- Why the simplex method is needed
- Moving from graphical solutions to algebraic
- Demonstrating how the simplex method works with a simple example
In the first article of this series, we went over how the attributes of linear programming allow it to only consider the corner points of constraints as potential optimal solutions. This is a very powerful feature that narrows an infinite solution space to a finite solution space. In the examples we reviewed, we only had a few constraints and a few variables — we even solved some of them by hand! After looking at…