Simplex Method | Introduction to optimization theory

In this video, I take you through a deep dive into the Simplex Method, which serves as a cornerstone of optimization theory. I begin by breaking down the essential terminology you need to set up any linear programming problem, specifically focusing on how to use slack and surplus variables to transform inequalities into standard equations. I also clarify the algebraic concepts behind basic solutions and basic feasible solutions so you have a solid foundation before we start calculating. From there, I walk you through a complete, step-by-step example of a maximization problem to show you exactly how the process works in practice. I make sure to address the tricky "what-if" scenarios that often confuse students, such as how to handle infinity or negative values when they appear in your ratio tests. Finally, I explain the concept of degeneracy, showing you how to identify a tie in the minimum ratio and what that means for your iterations. My goal is to make these complex mathematical shifts feel intuitive and manageable.