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Linear minimization problem

  1. Dec 28, 2011 #1
    Hi all,

    does anyone know what type of problem this would be classified as, and what kind of algorithm I could use to get a solution?

    minimize:
    P=60w1+30w2+10w3+100w4

    subject to:
    P ≥ 50
    0 < wi ≤ 1

    thanks very much
     
  2. jcsd
  3. Dec 29, 2011 #2

    mathman

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    What are you trying to minimize? Without this, the question is incomplete. Defining what you want to minimize with these conditions is called linear programing.
     
  4. Dec 29, 2011 #3

    AlephZero

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    It looks like a Linear Programming problem. The most straightforward solution algorithm is the Simplex Method.
     
  5. Dec 30, 2011 #4

    HallsofIvy

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    The fundamental result in "linear programming" is that a minimum or maximum of a linear function, in a convex polyhedron, must occur at a vertex of the polhedron. Your condition, [itex]0< w_i\le 1[/itex], says that the "feasible region" is a n-dimensional rectangle and it is easy to calculate its [itex]2^n[/itex] vertices. However, the condition S> 50, on the target function will have to be applied after determining values. Also the fact that the faces [itex]0= w_i[/itex] are NOT in the feasible region can be a problem.
     
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