LP4

Finding the Optimum Point Graphically for a Two-Phase Linear Program

Recall the Acme Bicycle Company Example that was discussed in the notes and previous examples: 

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 revis...
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