The Busing Problem
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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?