LP3

Using the Simplex Tableau

The simplex method is a simple and elegant algorithmic engine for solving linear programs. This example demonstrates its mechanics.  The animation solves the Acme Bicycle Company example using the simplex tableau. The Acme Bicycle Company formulation is repeated below.

Variables:

  • x₁: mountain bikes to produce (bikes/day)
  • x₂: racers to produce  (bikes/day)

Variable non-negativity:

  • x₁ ≥ 0,  x₂ ≥ 0

Objective Function:

  • Maximize daily profit ($/day):  Max Z =  15 x₁ + 10 x₂

Constraints:

  • Mountain bike production limit (bikes/day): x₁ ≤ 2
  • Racer production limit (bikes/day): x₂ ≤ 3
  • Metal finishing machine production limit (bikes/day): x₁ + x₂ ≤ 4

 



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Contents

Chapter 1: Introduction.  An introduction to the process of optimization and an overview of the major topics covered in the course.  Last revision: December 2020 . Chapter 2: Introduction to Linear Programming.  The basic notions of linear programming and the simplex method. The simplex method is the easiest way to provide a beginner with a solid understanding of linear programming.  Last revision: December 2020. See animation  LP1 . A good  article on formulating LPs  by Gerry Brown and Rob Dell. Example questions with solutions . March 4, 2021. Chapter 3: Towards the Simplex Method for Efficient Solution of Linear Programs.  Cornerpoints and bases. Moving to improved solutions.  Last revision: December 2020 . See animation  LP2 . Chapter 4: The Mechanics of the Simplex Method.  The tableau representation as a way of illustrating the process of the simplex method. Special cases such as degeneracy and unboundedness.  Last revision: December 2020. See animation  LP3 . Example questions
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