Publication: Journal of Economic Education
Volume: 36, Number 1
Issue: Winter 2005
Pages: 100
Author(s): R. Scott Harris
Address (Principal Author):
R. Scott Harris
Montana State University-Billings
1500 University Drive
Billings, MT 59101
Fax Number: 406-657-2327
Office Phone: 406-896-5822
Internet Address (Principal Author): sharris@msubillings.edu
Title: Linear Programming Graphic Tutorial
URL: http://www.msubillings.edu/sharris/LP_Problem_intro.htm
Descriptive Note:
Linear programming (LP) affords the teacher a simple yet powerful way to demonstrate applications of constrained optimization. As such, it can be an effective pedagogical and demonstration tool in Intermediate Microeconomic Theory and other upper-division courses. Often an introduction to LP is included in a Managerial Economics course, Quantitative Methods course or in Operations Management.
As they learn LP, students may miss the fundamental economics principles by concentrating on demystifying the mathematics. Many textbooks stress geometric expositions using two variables and static graphics. Because even the simplest LP problem can result in a fairly complex set of static graphics, adapting the exposition to an animated step-by-step Flash™ presentation renders major improvements in pedagogical technique.
This tutorial solves a simple problem by breaking it into separate step-by-step parts that students can assimilate and review at their own pace. After a brief introduction to constrained optimization and the demonstration problem, the first two parts of the tutorial separately develop the objective function and the feasible (constraint) area through a combination of simple algebra and animated geometric expositions. In the third part, the objective function line is superimposed over the feasible space and shifted to arrive at the optimization solution. The last part of the tutorial demonstrates a few applications of sensitivity analysis. Students also can download a solution spreadsheet for Excel.
The tutorial should be viewed many times for different purposes. Introducing students to the general concepts of the linear programming-constrained optimization process may be best accomplished initially by concentrating solely on the overall geometric exposition. After the students grasp the basic idea of the process, they should learn how the algebraic specification of the problem is integrally tied to the geometric exposition. Finally, they should acquaint themselves with the terminology and nuances of LP including the concept of slacks (unused resources, and sensitivity analysis.
R. Scott Harris is Associate Professor of Economics at Montana State University Billings.
Winter 2005 Table
of Contents
Online Section
Journal of Economic
Education WWW Page