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Homework Help: Limit problem, with mins, I know the answer already and I know it is right. But the l

  1. Sep 20, 2011 #1
    1. The problem statement, all variables and given/known data

    Given the follow LOP P

    I am just going to write down the obj function because that is most important for my question and the constraints aren't

    [tex]w = y_1 - 2y_2 + y_3[/tex]

    I was asked to show that [tex]y = (2t, 3t,t)^t[/tex] is a solution for all [tex]t\geq 0[/tex]

    So w = 2t - 2(3t) +t = 2t - 6t + t = -4t + t = -3t

    Now initally I thought that as [tex]t \to \infty [/tex], [tex]-3t \to -\infty [/tex]

    I checked the key provided by my prof and he took [tex]t \to -\infty [/tex] and [tex]-3t \to \infty [/tex]

    Is it because we always assume w >0?

    The flaw I made is that I never consider [tex]t \to \pm \infty [/tex].




    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 21, 2011 #2

    Mark44

    Staff: Mentor

    Re: Limit problem, with mins, I know the answer already and I know it is right. But t

    In applied problems, the objective function is usually nonnegative, but in more theoretic presentations, I don't see why this needs to be true.
     
  4. Sep 21, 2011 #3
    Re: Limit problem, with mins, I know the answer already and I know it is right. But t

    I asked my prof today and he kinda said the same thing about "yes intuitively that is right, we want obj f > 0". Then he added a bunch of things that confused me even more...

    He stated something like this

    max z = -min(-z)
     
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