Investigacion Operativa Taller 1

 

Reovbrsodnd Mbetrni dbi Bmundhr Cnmuitnd db Mobemons Bmheýaomns Oevbsgnmoýe Hpbrnvn Eha`rb< Kbvoe Dbigndh Nuin< ::0 >.

Ren cî`romn db qubshs prhdumb trbs tophs db qubshs< qubsh murndh, qubsh sbaomurndh y qubsh crbsmh. Znrn biih sb utoiozne dhs tophs db ibmfb, ibmfb db hvbln y ibmfb db mn`rn. In cî`romn bstî dhtndn db dhs tophs db aîquoens. In aîquoen >, utoiozn be mndn fhrn 7: iotrhs db ibmfb db hvbln y 0:: iotrhs db ibmfb db mn`rn mn`rn pnrn pnrn prh prhdum dumor or ? koi koihgr hgrnah nahss db qubsh qubsh mur murndh ndh,, 0 koi koihgr hgrnah nahss db qubsh qubsh sba sbaomu omurnd rndh h y 2 koihgrnahs db qubsh crbsmh. Mhe in aîquoen 0, sb h`tobebe mndn fhrn >:, 2 y 4 koihgrnahs db mndn qubsh rbspbmtovnabetb mhe ue gnsth db >:: iotrhs db ibmfb db hvbln y 6: iotrhs db ibmfb db mn`rn. Tbeobedh be mubetn ihs bstudohs db dbanedn db ihs trbs prhdumths in mhapnþán bstoan qub db`b  prhdumor ni dán ni abehs ?:: y =:: koihgrnahs db qubsh murndh y sbaomurndh, rbspbmtovnabetb, y eh aîs db 6:: koihgrnahs db qubsh crbsmh. Ihs `bebcomohs phr koihgrnah prhdumodh db mndn toph db qubsh she db 4, 3, y 7 dýinrbs rbspbmtovnabetb. In gbrbemon db in baprbsn sb fn pinetbndh ins soguobetbs abtns y h`lbtovhs mhe bi soguobetb hrdbe db  prohrodndbs< 

Zrohrodnd >. In mnetodnd db ibmfb utoiozndn pnrn in prhdummoýe db ihs qubshs eh supbrb >4:::

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iotrhs donrohs pnrn in ibmfb db hvbln y 0:::: iotrhs donrohs pnrn in ibmfb db mn`rn. Zrohrodnd 0. In mnetodnd db ibmfb db mn`rn eh sbn supbrohr n in db hvbln.



Zrohrodnd =. Anxoaoznr `bebcomohs.

Ahdbioznr y rbshivbr bi prh`iban pnrn mnimuinr bi eüabrh db fhrns ni dán qub db`be hpbrnr ins aîquoens. Cuemoýe h`lbtovh< Anxoaoznr ihs `bebcomohs Snron`ibs<

 V > ← V  Koihgrnahs^ubshMurndh ( Anquoen  Anquoen > )  V 0 ← V  Koihgnrahs ^ubsh ]baomurndh ( Anquoen > )  V = ← V  Koihgrnahs^ubsh Crbs Crbsmh mh ( Anquoen > )  V 4 ← V  Koihgnrahs ^ubsh Murndh ( Anquoen 0 )  V 2 ← V  Koihgrnahs^ubsh ]baomurn ]baomurndh dh ( Anquoen 0 )  Koihgrnahs ^ubsh Crbsmh  Anquoen 0  V 3 ← V  Koihgrnahs ( )

 

Reovbrsodnd Mbetrni dbi Bmundhr Cnmuitnd db Mobemons Bmheýaomns Oevbsgnmoýe Hpbrnvn Eha`rb< Kbvoe Dbigndh Nuin< ::0 Ahdbih antbaîtomh<

 Aoeoaoznr \ 14 V >+ 3 V 0 + 7 V = + 4 V 4 + 3 V 2 + 7 V 3 ]ulbth n< ? V >

+ >: V  ≢ ?:: ( Koihgrnahs  Koihgrnahsdb db qubshmurndh qubsh murndh )

0 V 0

+2 V  ≢ =:: ( Koihgrnahsdb qubsh sbao murndh)

2 V =

+ 4 V  ≢ ?:: ( Koihgrnahs db qubsh crbsmh)

? V >

+0 + 2 V  + >: V  +2 V  +4  V  ≤ >4::: ( Iotrhs db ibmfb db hvbln hvblndonrohs donrohs )

? V >

+ 0 V  + 2 V  + >: V  + 2 V  + 4 V  ≤ >4::: ( Iotrhs db ibmfb db mn`rn mn`rndonrohs donrohs )

? V >

+0 V  +2 V  17: ( Iotrhs db ibmfb db hvbln phr fhrn)

4

2

3

=

0

? V >

=

2

4

3

2

3

=

0

>: V 4

4

+ 2 V  + 4 V  10:: ( Iotrhs db ibmfb db mn`rn phr fhrn ) 2

3

+2 V  + 4 V  1>:: ( Iotrh  Iotrhss db ibmfb db hvbln phr fhrn)

>: V 4

0

=

+ 2 V  + 4 V  16: ( Iotrhsdb ibmfb db mn`rn phr fhrn ) 2

3

Mhedomoýe db eh ebgntovodnd<

 V > + V 0+ V = + V 4 + V 2 + V 3 5 :

 

Reovbrsodnd Mbetrni dbi Bmundhr Cnmuitnd db Mobemons Bmheýaomns Oevbsgnmoýe Hpbrnvn Eha`rb< Kbvoe Dbigndh Nuin< ::0

0.

In mhapnþán @rhwe bs uen baprbsn pbqubþn. Db`odh n ihs sobaprb mrbmobetbs mhsth db trnesphrtb, in mhapnþán db`b tbebr bspbmoni muodndh be bi aneblh db sus hpbrnmohebs db trnesphrtb y beváh. In mhapnþán nmn`n db rbmo`or ue pbdodh db 0: bsmrothrohs y >3 absns. In baprbsn pubdb surtor bi pbdodh, bevonedh ihs nrtámuihs n pnrtor db dhs nianmbebs qub tobebe be in moudnd. Ihs mhsths db trnesphrtb nshmondhs mhe ihs dhs nianmbebs she< Nianmïe

Nianmïe 0

> Bsmrothroh Absn

$=: $>4

$04 $>6

In mhapnþán betrbgn thdhs ihs pbdodhs utoioznedh sus prhpohs mnaohebs. Be bi nianmïe 0 sb bapibne mnaohebs db tnanþh abdoh; phr tneth, eh sb pubdbe trnesphrtnr aîs db 0: absns y bsmrothrohs. Be bi nianmïe >, sb pubdbe bevonr fnstn 06 absns y bsmrothrohs be ue shih mnaoýe, dndh qub sb utoiozne mnaohebs grnedbs. In mhapnþán fn bemhetrndh qub in phiátomn db hpbrnmoýe mhe anyhrbs gnenemons mhesostb be anetbebr aîs h abehs bi aosah oevbetnroh be ihs dhs nianmbebs; be bsths ahabeths bxostbe oevbetnrohs `nstnetb bquoio`rndhs be ihs nianmbebs. Znrn anetbebr in phiátomn db oevbetnrohs, muniquobr hrdbe db beváhs db`b sbr tni qub in docbrbemon be bi eüabrh thtni db absns y bsmrothrohs qub sb beváne db muniquobr nianmïe eh pubdb bxmbdbr db dhs. ]b quobrb aoeoaoznr ihs mhsths thtnibs db trnesphrtb.

Cuemoýe h`lbvh< Aoeoaoznr ihs mhsths thtnibs db trnesphrtb Snron`ibs<

 V > ←Bsmrothrohsnianmbe >  V 0 ← Bsmrothrohs Bsmrothrohs nianmbe0  V = ← Absns Absns nianmb nianmbe e>  V 4 ← Absns Absns nianmb nianmbe e0 Ahdbih antbaîmh< Aoeoaoznr \ 1=: V > + 04 V 0 + >4  V = + >6 V 4 ]ulbth n<

 V > + V 010: ( Bsmrothrohs n betrbgnr )  V = + V 41 >3 ( Absns  Absns n betrbgnr )

 

Reovbrsodnd Mbetrni dbi Bmundhr Cnmuitnd db Mobemons Bmheýaomns Oevbsgnmoýe Hpbrnvn Eha`rb< Kbvoe Dbigndh Nuin< ::0

 V 0 + V 4 ≤ 0: ( Mnp Mnpnm nmodn odnd d dbtrne s ph phrtb rtb db Bs Bsmro mrothr throhs ohs y Absnsninan Absnsninanmb mbe e 0)  V > + V = ≤ 06 ( M np npnmo nmodnd dnd db trne trne s phrtb phrtb db Bs Bsmro mrothr throhs ohs y Absns Absns nianmb nianmbe e >)  V 0 + V 4 ≤ 0 ( Doc betrbbi euabrh euabrh thtni db absns y bsmr n bevonr dbsdb bi nianmbe> )  V > + V = ≤ 0 ( Doc  Doc betrb betrb bi euabrh euabrh thtni db absns y bsmr n bevonr dbsdbbi nianmbe 0 ) Mhedomoýe db eh ebgnvodnd<

 V > + V 0+ V = + V 4 5 :