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3 - Graphical Linear Programming

Published online by Cambridge University Press:  11 March 2021

David C. Vella
Affiliation:
Skidmore College, New York
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Summary

In this chapter, we introduce linear programming. We start with a simple algebra problem that can be modeled as a system of equations. However, that problem has no solution, so we modify the model to make it more realistic. The result is a standard form linear programming problem. This shows how linear programming arises naturally from the modeling process. Next, we show how to solve these problems in the case when there are two decision variables by the standad graphical technique, which we call graphing in the decision space. This leads naturally to a discussion of the corner point theorem. Finally, we exhibit an alternate graphical approach to solving these problems in the case when there are just two constraints but an arbitrary number of decision variables. We call this method graphing in the constraint space. This technique is a feature of this text; it is not covered in most texts. It is based on linear combinations of vectors in a plane and basic solutions to systems of linear equations, and it sets the stage for the simplex algorithm in Chapter 5.

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Publisher: Cambridge University Press
Print publication year: 2021

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  • Graphical Linear Programming
  • David C. Vella, Skidmore College, New York
  • Book: Invitation to Linear Programming and Game Theory
  • Online publication: 11 March 2021
  • Chapter DOI: https://doi.org/10.1017/9781108568166.005
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  • Graphical Linear Programming
  • David C. Vella, Skidmore College, New York
  • Book: Invitation to Linear Programming and Game Theory
  • Online publication: 11 March 2021
  • Chapter DOI: https://doi.org/10.1017/9781108568166.005
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Graphical Linear Programming
  • David C. Vella, Skidmore College, New York
  • Book: Invitation to Linear Programming and Game Theory
  • Online publication: 11 March 2021
  • Chapter DOI: https://doi.org/10.1017/9781108568166.005
Available formats
×