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What means binding in equilibrium ?

  1. May 13, 2009 #1
    what means "binding in equilibrium" ?

    hi there,
    im a german student and ive come across a phrase that is:
    (2) and (5) are binding in equilibrium, and (3) and (4) are slack.


    2,3,4,5 are given equations, but
    can anyone explain that to me, so i can, without any knowloedge of the special mathematic vocabulary in english, translate it myself?
    i know what an equilibrium is, but the rest i dont, specially not the context.

    PLEASE help!
    THX
     
  2. jcsd
  3. May 14, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi Schreiber! Welcome to PF! :smile:
    hmm :rolleyes: … this looks as if it comes from OR, or linear programming.

    I think the difference is between binding constraints (or equations) and slack constraints (or inequations) …

    an equation with = is binding, but if it has < or ≤, it is slack …

    and a slack (in)equation can be turned into a binding equation by inserting a "slack variable" (which personally I'd call a "dummy variable") …

    for example, from http://en.wikipedia.org/wiki/Slack_variable
    … where (I think :redface:) Ax ≤ b is slack but Ax + y = b is binding.

    see also http://en.wikipedia.org/wiki/Linear_programming#Augmented_form_.28slack_form.29
     
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