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I have question&its solutiion but how?in LP

  1. Mar 19, 2009 #1
    Blending problem:
    Decision variables
    x1: tons of ore from mine 1 in each ton of the blend
    x2: tons of ore from mine 2 in each ton of the blend
    x3: tons of ore from mine 3 in each ton of the blend
    x4: tons of ore from mine 4 in each ton of the blend
    Objective function
    Min cost
    Min 800x1+400x2+600x3+500x4
    Constraints
    Element A: 10x1+3x2+8x3+2x4>=5
    Element B: 90x1+250x2+75x3+175x4>=100
    Element C: 45x1+25x2+20x3+37x4>=30
    Weight: x1+x2+x3+x4=1

    If you know that Element B has slack of 31.666
    x1=0.259259
    x2=0.703705
    x3=0.037037
    x4=0.00000
    there is a question
    what is the amount used of element B?compute it

    i found a solution please if it is right can anyone explain it to me

    90*0.259259+250*0.703705+75*0.037037+175*0-31.66=100

    therefore the amount used =131.66

    Can anyone Explain it to me?
     
  2. jcsd
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