Where Is the Highest Point on the Roof of a Shed?

Abstract

Some time ago, a freshman engineering student returned to the high school where I taught and described to me some of his struggles with university mathematics. The simplex method of linear programming was one topic that we discussed. This student could perform the mechanics of the simplex method—finding pivot columns, pivot rows, and row reductions; however, he confessed that he had no idea why the simplex method worked to find the maximum point. Moreover, he could not connect the theorems that his professor proved in the lectures with the simplex method. So I asked him this question: “Where is the highest point on the roof, excluding the overhang, of a shed with a plane, but sloping, roof?” He looked at me and was clearly wondering why sheds had anything to do with linear programming.