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Is this a trick question? Standard form

  1. Sep 18, 2011 #1
    1. The problem statement, all variables and given/known data

    [PLAIN]http://img191.imageshack.us/img191/7440/unledtev.png [Broken]


    3. The attempt at a solution

    There are like 2 other problems in my book similar to this one.

    I thought problems posed in this manner are already in standard form. They say

    "max [obj f]

    s.t.

    constraints, for variables positive "
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Sep 19, 2011 #2

    Ray Vickson

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    I hope your book does not say that variables are positive, for often they are not: they can be ZERO as well, and often are in an optimal solution. So, you should say non-negative, not positive. Problems with positive variables may not have any optimal solutions; the simplest example of this is min x, subject to x > 0.

    Does the problem above satisfy ALL the requirements of a "standard" problem?

    RGV
     
    Last edited by a moderator: May 5, 2017
  4. Sep 19, 2011 #3
    Oh I have change [tex]3x_1 +3x_2 + x_3 \geq 2[/tex] to [tex]-3x_1 - 3x_2 - x_3 \leq -2[/tex]

    And for [tex]x_1 + 2x_3 = -4[/tex], I have to change it to [tex]-x_1 - 2x_3 \leq 4[/tex] because x_1 and x_3 are nonnegative ?

    Also what does u.r.s. mean...? Because I just assumed it meant it can be positive..

    EDIT:

    [tex]x_1 + 2x_3 = -4[/tex]

    Could also say

    [tex]x_1 + 2x_3 \geq -4[/tex] and [tex]x_1 + 2x_3 \leq -4[/tex]

    Then

    [tex]-x_1 -2x_3 \leq 4[/tex] and [tex]x_1 + 2x_3 \leq -4[/tex] would make the requirements for constraints in standard form.
     
  5. Sep 19, 2011 #4

    Ray Vickson

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    Different authors have different definitions of "standard form". For example, the standard form in https://netfiles.uiuc.edu/angelia/www/ge330fall09_stform4.pdf [Broken] is max or min cx, st AX = b, x >= 0 (obtained by using slack or surplus variables if necessary). In others sources the standard is a minimization, in some others a maximization, in some others the constraints must all be <=, etc. Myself, I prefer the form max cx st Ax=b, x >= 0 form, because that is the form you need to get started on the simplex method. However, *ALL sources agree that 'x >= 0' is part of the standard*.

    In your problem, x_3 urs means, I think, that x_3 is unrestricted in sign; that is, x_3 can be < 0 or >= 0. That makes your problem non-standard, and you are asked to do something to it to put it into standard form. More than that I cannot say without solving your problem for you.

    RGV
     
    Last edited by a moderator: May 5, 2017
  6. Sep 19, 2011 #5
    It does say (max) in parenthesis, let's go with mine!

    Oh that's easy, I can just make it into positive as I have and erase my new inequality!

    Thanks
     
    Last edited by a moderator: May 5, 2017
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