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Math Help - Simpleg Algorithm LP trouble.

  1. #1
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    Simpleg Algorithm LP trouble.

    Vinery 1 can produce 30 boxes per day.
    Vinery 2 can produce 20 boxes per day.
    Fred's needs at least 20 boxes a day.
    Kevin's needs at least 18 boxes a day.
    Mark's Needs only 5 boxes a day.

    COSTS: Fred's Kevin's Mark's
    Vinery 1 35 62 65
    Vinery 2 28 36 33

    Determine min cost delivery scheme that satisfies needs of bottle shops and does not exceep production capacities.


    I have defined my decision variables:
    X1= number of boxes from Vinery 1 to Fred's
    X2= number of boxes from Vinery 2 to Fred's
    X3= number of boxes from Vinery 1 to Kevin's
    X4= number of boxes from Vinery 2 to Kevin's
    X5= number of boxes from Vinery 1 to Mark's
    X6= number of boxes from Vinery 2 to Mark's

    Objective function:
    min Z = 35X1 + 28X2 + 62X3 + 36X4 + 65X5 + 33X6

    and my constraints:
    X1 + X2 >= 20
    X3 + X4 >= 18
    X5+ X6 = 5
    X1 + X3 + X5 <= 30
    X2 + X4 + X6 <= 20
    X1,X2,X3,X4,X5,X6 >= 0

    Question: Are these the right variables and constraints, and how do i proceed from here?
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  2. #2
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    Re: Simpleg Algorithm LP trouble.

    I think you'd get more responses if you posted this in the business math sub-forum.

    In any case, it seems like what you have is correct so far. I'm pretty sure there are other ways to do this (and I may be wrong), but here's what I got for x1,x2,...,x6: 20,0,3,15,0,5 respectively.

    I started with X5+X6=5. Just considering Mark, the minimum cost will be if all 5 come from Vin2 and none from Vin1. Now, if we get 1 from Vin1, the cost increases by 65-33 = 32. But it's not possible to get a combination (considering Fred and Kevin as well) that will save at least that much, so X5=0 and X6=5.

    Now, looking at X1 to X4, delivering to Kevin from Vin2 instead of Vin1 will save 62-36 = 26, whereas delivering to Fred from Vin2 instead of Vin1 will save 35-28 = 7. So, send the most you can to Kevin from Vin2, this gives us X4 = 15 (since 5 of the 20 from Vin 2 goes to Mark), and X3 = 3 (so that Kevin gets his minimum 18).

    That leaves us with 20 going to Fred from Vin1, and none going to Fred from Vin2.

    After that, I just played around abit with the numbers and saw that what I got gives the minimum ... so I may be wrong
    Last edited by Bingk; April 17th 2012 at 03:47 AM.
    Thanks from linalg123
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