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. In addition to the lesson plan, the site includes ideas for assessment, teacher discussion, extensions of the lesson, additional resources, and a discussion of the mathematical content. The lesson plan is accompanied by video clips illustrating lesson procedures. The user should first locate the Busing Problem lesson and then access the appropriate video clips. (author/pk)

Linear programming is one of the most widely used applications of mathematics with uses in business planning, industrial engineering, and social and physical sciences. Because of the complicated and advanced nature of the lesson presented, career-technical and mathematics teachers might consider working together to present and apply the lessons. The problems themselves are presented in an interesting and compelling way, and career-technical teachers will find that they can easily adapt the situation to almost any career focus. In agriculture, the question might be how to allocate crop acreage for maximum profit and maximize the use of expensive equipment. In business, the question might be how best to focus sales efforts. The scheduling of employees can be used to illustrate the application of the concept in any career focus. The High School Operations Research web page has four topic modules that also deal with linear programming, each of which has several associated case studies that report on the use of linear programming in real business situations from McDonald's to farming. The case studies that are presented will help students understand the application of this mathematical model.