Introduction

Many STEM majors would be well-suited to study optimization or, more broadly, industrial engineering, in graduate school, but most are not aware of this exciting, in-demand field. We envision Linear Algebra students as the primary target for this module because students who are studying Linear Algebra are also a likely audience for optimization, and because Linear Algebra is so fundamental to the study of optimization. We seek to introduce the field of optimization to these students through an engaging activity that both reinforces concepts from Linear Algebra and develops a conceptual framework that will be useful for students who go on to study optimization in a later course.

After a fun, hands-on activity, we introduce optimization modeling and a simple (albeit computationally expensive) algorithm for solving linear optimization models, commonly called Linear Programs or LPs, with bounded feasible regions. The algorithm relies on the basic geometry of systems of linear inequalities. The ideas in this simple algorithm are fundamental to the Simplex Method, the linear optimization algorithm that is implemented in commercial optimization solvers and that is typically taught in a first course in optimization.