PBS Teachers™

PBS Teachers

Multimedia resources & professional development for America's preK-12 educators.


The Busing Problem
Linear Programming

Download PDF Lesson | Get Acrobat
A Printable version of this lesson is available in PDF format
This requires a free plug-in, Adobe Acrobat Reader.
You can find out if you need it by clicking on the PDF link.


Students use substitution and the elimination method to solve linear systems in order to solve linear programming problems.

Overview of the Lesson

In this lesson, the students solve two linear programming problems. The first one. Researching Research Papers, involves three variables; the second, The Busing Problem, involves four variables. During the lesson, students work together to solve problems by exchanging ideas, organizing information, and sharing that information with the entire class. Students apply the substitution method and the elimination method to solving linear systems, which allows them to identify the corner points of the feasible regions. All of these corner points are tested in the equation that is to be maximized or minimized, depending on the particular problem situation. After solving the problems, students conclude that the problems with four variables are complex and very tedious to solve. This prepares them for using matrices and the graphing calculator to solve systems in Meadows or Malls? lesson that follows. Because of the sequential nature of the lessons, The Busing Problem should be done before Meadows or Malls?