Johnathan Harrell, Kiah Epperson, Bailey Trytek, & Dr. Ivona Grzegorczyk
Linear programming, also known as linear optimization, plays a pivotal role in resource allocation and decision-making across various fields. In this study, we concentrate on the powerful simplex method that is currently widely used and may involve many variables. This method is an example of optimization problem for functions (representing resources) with domains restricted by linear constrains. The shape of the domain is polygonal (or looks like a simplex in several dimensions). The process navigates through multiple variables to identify the most efficient utilization of resources in achieving desired outcomes. We aim to elucidate the mechanics of the simplex method and showcase examples of real-world applications. We provide visualization in the case of two variables. For more variables the method used matrices and row reduction to find the optimal answer (hence computers can solve these types of problems). By exploring its functionality and practical implications, we unveil the versatility and effectiveness of the simplex method as a tool for optimization in many different environments.