tut4 - Converting a Linear Program to Standard Form In this...

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1 Converting a Linear Program to Standard Form Cleaver, an MIT Beaver In this tutorial, we briefly explain what standard form is, and how to convert a linear program to standard form
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2 Linear Programs in Standard Form We say that a linear program is in standard form if the following are all true: 1. Non-negativity constraints for all variables. 2. All remaining constraints are expressed as equality constraints. 3. The right hand side vector, b, is non-negative. maximize z = 3x 1 + 2x 2 -x 3 + x 4 x 1 + 2x 2 + x 3 -x 4 5 ; -2x 1 -4x 2 + x 3 + x 4 -1; x 1 0, x 2 0 An LP not in Standard Form not equality not equality, and negative RHS x 3 and x 4 may be negative
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3 And … Tim, the turkey Isn’t this exactly the same as was done in Lecture 4 of 15.053? Yes. I’m repeating some of the material from Lecture 4. But, I’m also adding some new material.
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4 s 1 is called a slack variable , which measures the amount of “unused resource.” Note that s 1 = 5 - x 1 -2x 2 -x 3 + x 4 . Converting Inequalities into Equalities
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This note was uploaded on 01/18/2012 for the course MANAGEMENT 15.053 taught by Professor Jamesorlin during the Spring '11 term at MIT.

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tut4 - Converting a Linear Program to Standard Form In this...

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