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HW Sol Due 3-12-2009

HW Sol Due 3-12-2009 - Problem 13 Solving a simultaneous...

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Unformatted text preview: Problem 13 Solving a simultaneous system of equations is not necessary for this problem since it can be solved in a straightforward manner: 11:10 2.2 :O+—?i,tl =75 4 213 =O+iil +212 =2.5+7.5=10 Problem 14 The system of equations relating these mean flow rates are: 1 1 i=10+§iz+gi3 3 12 "10+le 1 2 l=0+mz+ml 3 4 1 3 2 and the from/to probability matrix is: 0 [3/4 1/4 P: 1/3- 0 2/3 1/5 0 0 The system becomes (I—PUé = 7 1 1 i—gn—Eifdo --:-;t,+;t2+0/‘L3 =0 sill-it. +34% +33 = 0 The solution &=(I-PT)‘17’ via a compute code is: external inflows by workstation (gem): { 10, 0, workstation from/to branching probabilities (P) 0.0000 0.7500 0.2500 0.3333 0.0000 0.6667 0.2000 0.0000 0.0000 system of equations relating flow rates (lam) M.lam = gem; where M = I—TransposeHPJ M 1.0000 -0.3333 —0.2000 ~0.7500 1.0000 0.0000 -0.2500 —0.6667 1.0000 lam: { 16.6667, 12.5000,r 12.5000} 0} ...
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