Table of Contents
CSE 589 Part IV
Readings
Linear Programming
Big Bucks!
And more...
Feasible Set
An example: The diet problem
Visually… x= peanut butter, y = steak
Optimal vector occurs at corner of feasible set!
Optimal vector occurs at corner of feasible set!
General Form of a Linear Program.
The Feasible Set
The Simplex Method
Simplex Algorithm: An Example in 3D
Example of Simplex Method, continued.
Example of Simplex Method, continued.
Example of Simplex Method, continued.
Example of Simplex Method, continued.
The Simplex Method
What were we doing?
The Simplex Algorithm and beyond….
A Central Result of LP Theory Duality Theorem
Primal: Minimize cx
subject to Ax >= b, x>= 0Dual: Maximize yb subject to yA <=c, y>=0
An example: The diet problem
Simple Example
More general diet problem
Example
What’s going on?
Duality Theorem
For [x(st), x(pb)] and [y(s-prot), y(s-carbo)] feasible =>
Practical Use of Duality
Formulate as LP
Application: Optimal Pipeline
Summary of Linear Programming
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Author: Anna Karlin
Email: karlin@cs.washington.edu
Home Page: http://www.cs.washington.edu/education/courses/589
Download presentation source
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