Tugas RO Print
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1. Shortest Path
2. Maximum Flow
x0xs01
xs02
xs03 x12 x1si x2si x32 x3si sum rhs
initial 40 20 10 10 0 20 15 5 5
s0 1 -1 -1 -1 0equa
l 0
1 1 -1 -1 0equa
l 0
2 1 1 -1 1 0equa
l 0
3 1 -1 -1 0equa
l 0
si -1 1 1 1 0equa
l 0
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ty
3. Critical Path Method
$ x1 x2 x3 x4 x5 x6 rhs
0 1 1 1 1 1 1
&'t( & -1 1 0 "= 6
&'t( ) -1 1 0 "= 9&'t(
Dummy 1 -1 0 "= 0
&'t( C -1 1 0 "= *
&'t( D -1 1 0 "= +&'t( , -1 1 0 "= 10
&'ti( -1 1 0 "= 10
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Microsoft Excel 14.0Answer e!ort"or#sheet$ %tu&as'.xlsx(Sheet1e!ort Created$ 3)11)201*+$2,$4- PMesult$ Soler has coner&ed to the current solution. AllConstraints are satis/ed.
Soler En&ine
,n.ine/ onlinearSolution #ime/ 1625Secons!terations/ 1+ Suprolems/0
Soler '!tionsax #ime nlimite7 !terations nlimite7 8recision0000001Con(er.ence 000017 8opulation Si$e 07 anom See 07 Deri(ati(esorarax Suprolems nlimite7 ax !nte.er Sols nlimite7 !nte.er #olerance 1:7 &ssumeone.ati(e
;ecti(e Cellin>
Cell ame'ri&inalalue
Finalalue
?)?22
totalcost "= 110030 5
@ariale Cells
Cell ame'ri&inalalue
Finalalue
nte&er
?)?13 1 0 Contin?C?13 1 1
Contin
?D?13 1 0
Contin
?,?13 1 0
Contin
?? 1 0 Conti
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13 n?)?14 1 1
Contin
?C?14 1 0
Contin
?D?14 1 0
Contin
?,?14 1 0
Contin
??14 1 0
Contin
?)?15 1 0
Contin
?C?15 1 0
Contin
?D?15 1 0
Contin
?,?15 1 1 Contin??15 1 0
Contin
?)?16 1 0
Contin
?C?16 1 0
Contin
?D?16 1 1
Contin
?,?16 1 0
Contin
??16 1 0
Contin
?)?1+ 1 0
Contin
?C?1+ 1 0
Contin
?D?1+ 1 0
Contin
?,?1+ 1 0
Contin
??1+ 1 1
Contin
Constraints
Cell ame Cell alue FormulaStatus
Slac#
?)?1* rhs 1
?)?1*"=?)?20
)inin. 0
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?C?1* rhs 1
?C?1*"=?C?20
)inin. 0
?D?1* rhs 1
?D?1*"=?D?20
)inin. 0
?,?1* rhs 1
?,?1*"=?,?20
)inin. 0
??1* rhs 1
??1*"=??20
)inin. 0
??13 rhs 1
??13
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esult$ Soler found a solution. All Constraints and o!timalitconditions are satis/ed.
Soler En&ine
,n.ine/ Simplex A8
Solution #ime/ 0125 Secons
!terations/ * Suprolems/ 0Soler '!tions
ax #ime nlimite7 !terations nlimite7 8recision 0000001ax Suprolems nlimite7 ax !nte.er Sols nlimite7 !nte.er #olerance 1:7 &ssumeone.ati(e
;ecti(e Cell ax>
Cell ame'ri&inalalue
Finalalue
?)?
3 initial x0 3 40
@ariale Cells
Cell ame'ri&inalalue
Finalalue nte&er
?C?3
initialxs01 1 20 Contin
?D?3
initialxs02 1 10 Contin
?,?
3
initial
xs03 1 10 Contin??3
initialx12 1 0 Contin
??3
initialx1si 1 20 Contin
?B?3
initialx2si 1 15 Contin
?!?3
initialx32 1 5 Contin
??3
initialx3si 1 5 Contin
Constraints
Cell ame Cell alue Formula StatusSlac#
??4 s0 sum 0
??4=??4 )inin. 0
??5 sum 0
??5=??5 )inin. 0
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??6 sum 0
??6=??6 )inin. 0
??+ sum 0
??+=??+ )inin. 0
??* si sum 0
??*=??* )inin. 0
?C?3
initialxs01 20
?C?3
