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Linear programming: How to find extreme points and extreme directions?

  1. Nov 25, 2012 #1
    Hi guys

    I'm reading a book about linear programming and network flows. In chapter 2 when it talks about convex sets and their analysis it talks about extreme points and extreme directions of a convex set. I understand the definitions of extreme points and extreme directions, but I don't know how I should find them. Unfortunately the book doesn't show how to find them with examples. :( I also don't know what a 'slack variable' is. I guess it must've been defined somewhere but I missed it :/

    Any helps would be appreciated.
    Last edited: Nov 25, 2012
  2. jcsd
  3. Nov 26, 2012 #2
    C'mon.. it's really an easy question. No one here has ever passed a course in linear programming? really???
  4. Nov 26, 2012 #3


    Staff: Mentor

    It might be that the author is merely setting the stage by defining some terms before looking at some examples.
    Slack variables are used to turn constraint inequalities into equations. For example, if you have a constraint inequality 2x + 3y ≤ 10, you can rewrite this as 2x + 3y + a = 10, where a is a slack variable such that a ≥ 0.

    Generally you'll have one slack variable for each constraint inequality.

    If you keep reading, you'll probably run into some examples.
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