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I have question&its solutiion but how?in LP

by emadhamdy2002
Tags: howin, questionandits, solutiion
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emadhamdy2002
#1
Mar19-09, 12:45 PM
P: 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?
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