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Math Help - linear programming

  1. #1
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    Feb 2011
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    Lightbulb linear programming

    Hi, I really need some help on this! I've been working on the problem for about a week and I am not 100% sure that I found the right answer! Here's what I need to do:
    1. Max L(x1,x2,x3,x4)=32.5x1+60x2+50x3+225x4

    6 * x1 + 12 * x2 + 9 * x3 + 30 * x4 <= 9000
    15 * x1 + 12 * x2 + 9 * x3 + 144 * x4 <= 30000
    4 * x1 + 4 * x2 + 16 * x3 + 120 * x4 <= 16000

    x1>=0 x2>=10 x3>=30 x4>=0

    I have to solve this, but as you see x2>=10 and x3>=30, so here's what I did:
    Min L(x1,x2,x3,x4)=32.5x1+60x2+50x3+225x4

    6 * x1 + 12 * x2 + 9 * x3 + 30 * x4 <= 9000
    15 * x1 + 12 * x2 + 9 * x3 + 144 * x4 <= 30000
    4 * x1 + 4 * x2 + 16 * x3 + 120 * x4 <= 16000
    X5-X2<=-10 -X5+X2>=10
    X6-X3<=-30 -X6+X3>=30

    x1>=0 x2>=0 x3>=0 x4>=0 x5>=0 x6>=0
    I solved it and it looks fine!
    2. Now I need to write the normal form and solve it:
    Min L(x1,x2,x3,x4)=32.5x1+60x2+50x3+225x4

    6 * x1 + 12 * x2 + 9 * x3 + 30 * x4+x7 = 9000
    15 * x1 + 12 * x2 + 9 * x3 + 144 * x4+x8 = 30000
    4 * x1 + 4 * x2 + 16 * x3 + 120 * x4+x9 = 16000
    -X5+X2=10
    -X6+X3=30

    x1>=0 x2>=0 x3>=0 x4>=0 x5>=0 x6>=0
    I did it and it looks OK
    3. From the normal form I have to write the dual form and solve it. here's what I did:
    6*y1+15*y2+4*y3>=32,5
    12*y1+12*y2+4*y3+y4>=60
    9*y1+9*y2+16*y3+y5>=50
    30*y1+144*y2+120*y3<=255
    -y4<=0
    -y5=0
    y1=0
    y2=0
    y3=0
    y4=0
    y5=0

    What I get as answer from Excel Solver is: Solver could not find feasible solution! Is it possible? Could someone find any errors in my efforts? Am I right at all? I am completely lost now! Thanks for the help!
    Last edited by mimitheone; February 21st 2011 at 01:22 PM. Reason: Solved
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  2. #2
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    May 2010
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    Did you resolve this issue?
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  3. #3
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    Feb 2011
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    Yes, I did! As I was solving the problem, somehow Excel calculated something else! When I did the on calculation completely file, everything went smooth! Thanks for your attention!
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