Tarea Academica 3 Investigacion Operativa

 

Y OW HO OA OIH M MDDAO 1 DBZH QYDF OADLB L^H WOYDZO O^HKKDILQ T BLMGWHQ0 Kävobl Auyo Eotchrdbh Qhkhbh HQAXHKO0 Dbfhbdhrío Dbiustrdok

ADAKL0 ZDDD

^WLGKHMO >? (>6 pubtl)0 Adhrto kíbho ih prliuaadñb jogrdao ils prliuatls. Kls iotls phrtdbhbths oporhahb phrtdbhbths oporhahb hb ko prdmhro togko oi`ubto. Hk tdhmpl tdhmpl tltok idsplbdgkh idsplbdgkh (poro ko prliuaadñb y ko puhsto hb moraco) aoio shmobo hs ih 3> clros. Ko jdrmo bl tdhbh td hbh dbvhbtordl ih prliuatl okfubl ok prdbadpdl ih ko shmobo ?, y bl sh phrmdth quh q uh kl thbfo ok jdbok ih ko shmobo 9. Hk alstl ih albshrvor ubo ubdioi ih dbvhbtordl ih ubo shmobo o ko sdfudhbth hs ih $9 poro aoio prliuatl. Xbo ubdioi ih ihmobio bl sosjhaco auhsto $?> plr hk prliuatl O y $?8 plr hk prliuatl G. Kls iotls slgrh ko ihmobio oporhahb hb ko shfubio togko oi`ubto. Ko kíbho sh adhrro poro rhokdzor lphroadlbhs ih kdmpdhzo aoio jdb ih shmob shm obo. o. ^lr tobtl, sd ub prliua prliuatl tl hs jogrda jogrdaoil oil hb ko shmobo shmobo prhshbth prhshbth,, thbirï thbirï quh poforsh pofo rsh hk alstl alrrhsplbi alrrhsplbidhbth dhbth ok hmpl ih orrobquh orrobquh ihk hqudpl hb ko sdfudhbth sdfudhbth shmobo, shmo bo, sd hs quh sh ihadih jogrdaor ästh. Qñkl ub pl ih prliuatl prliuatl puhih jogrdaorsh jogrdaorsh iurobth ko shmobo. Bl puhih coghr prliuaadñb iurobth hk tdhmpl hb hk auok sh plbh hb moraco ko kíbho. Jlrmukh y rhsuhkvo hsth mlihkl ih pkobhoadñb ih 9 shmobos. Hk lg`hvl hs moxdmdzor kos fobobados hb hk phrdlil ih 9 shmobos.

 

!ZOWDOGKHQ0 Sd`e0 Xbdioihs hkoglroios ihk prliuatl d hb ko shmobo ` poro augrdr ko ihmobio ih ko shmobo e Td`0 Qh jogrdao l bl hk prliuatl d hb ko shmobo ` !JXBADLB LG@HYDZL5 MOS = 7>*(SO??+SO?7+SO?1+SO?9+SO77+SO71+SO79+SO11+SO19+SO99)+ 7>*(SO??+SO?7+SO?1+SO?9+SO77+SO71+SO79+SO11+SO19+SO99)+ 1>*(SG??+SG?7+SG?1+SG?9+SG77+SG71+SG79+SG11+SG19+SG99)(7>>*(TO?+TO7+TO1+TO9)+9>>*(TG?+TG7+TG1+TG9))(?>*(SO??+SO77+SO11+SO99)+?9*(SO?7+SO71+SO19)+?3*(SO?1+SO79)+77*(SO?9))(?8*(SG??+SG77+SG11+SG99)+?4*(SG?7+SG71+SG19)+71*(SG?1+SG79)+76*(SG?9))(?>*((3>-SO??)+(?>>-SO?7-SO77)+(68-SO?1-SO71-SO11)+(3>-SO?9-SO79-SO19SO99)))(?8*((?8-SG??)+(7>-SG?7-SG77)+(8>-SG?1-SG71-SG11)+(1>-SG?9-SG79-SG19SG99)))5 !WHQYWDAADLBHQ IH IHMOBIO5 SO??;=3>5 SG??;=?85 SO?7+SO77;=?>>5 SG?7+SG77;=7>5 SO?1+SO71+SO11;=685 SG?1+SG71+SG11;=8>5 SO?9+SO79+SO19+SO99;=3>5 SG?9+SG79+SG19+SG99;=1>>5 !XB QLKL YD^L IH ^WLIXAYL IXWOBYH KO QHMOBO5 TO?+TG?=?5 TO7+TG7=?5 TO1+TG1=?5 TO9+TG9=?5 !WHQYWDAADLBHQ IH YDHM^L IDQ^LBDGKH5 8*TO?+?>*TG?+>.8*(SO??+SO?7+SO?1+SO?9)+>.68*(SG??+SG?7+SG?1+SG?9);=3>5 8*TO7+?>*TG7+>.8*(SO77+SO71+SO79)+>.68*(SG77+SG71+SG79);=3>5 8*TO1+?>*TG1+>.8*(SO11+SO19)+>.68*(SG11+SG19);=3>5 8*TO9+?>*TG9+>.8*(SO99)+>.68*(SG99);=3>5 !^HWMDYDW AOBYDIOIHQ QLKL AXOBIL QH ^WLFWOMO ^WLIXAADLB5 SO??+SO?7+SO?1+SO?9;=(3>+?>>+68+3>)*TO?5 SO77+SO71+SO79;=(?>>+68+3>)*TO75 SO11+SO19;=(68+3>)*TO15

 

SO99;=(3>)*TO95 SG??+SG?7+SG?1+SG?9;=(?8+7>+8>+1>)*TG?5 SG77+SG71+SG79;=(7>+8>+1>)*TG75 SG11+SG19;=(8>+1>)*TG15 SG99;=(1>)*TG95 NFDB(SO??)5NFDB(SO?7)5NFDB(SO?1)5NFDB(SO?9)5 NFDB(SO77)5NFDB(SO71)5NFDB(SO79)5 NFDB(SO11)5NFDB(SO19)5 NFDB(SO99)5 NFDB(SG??)5NFDB(SG?7)5NFDB(SG?1)5NFDB(SG?9)5 NFDB(SG77)5NFDB(SG71)5NFDB(SG79)5 NFDB(SG11)5NFDB(SG19)5 NFDB(SG99)5 NGDB(TO?)5NGDB(TO7)5NGDB(TO1)5NGDB(TO9)5 NGDB(TG?)5NGDB(TG7)5NGDB(TG1)5NGDB(TG9)5

 

^WLGKHMO >7 (>6 pubtl)0 Hk hbtrhboilr Bdfct prhthbih hkhfdr ko okdbhoadñb dbdadok poro hk hqudpl ih gïsquhtglk. Hk hqudpl albsto ih sdhth `ufoilrhs quh hstïb akosdjdaoils (alb ubo hsaoko ih ? = mokl y 1 = hxahkhbth) ih oauhril alb su mobh`l ih gokñb, idsporls, rhglth y cogdkdioihs ihjhbsdvos. Kos plsdadlbhs quh o aoio hkhmhbtl sh kh phrmdth `ufor y kos aopoadioihs ihk `ufoilr sh kdstob hb ko sdfudhbth togko0

Kos okdbhoadlbhs dbdadokhs ih adbal `ufoilrhs tdhbhb q sosjoahr kos rhstrdaadlbhs sdfudhbths0 ?. ^lr kl mhbls mhbls auotrl auotrl mdhmgrls mdhmgrls ihghb shr aopoahs aopoahs ih `ufor hb ko ihjhbsdvo, ihjhbsdvo, plr kl mhbls ils hkhmhbtls ihghb dr o ko ljhbsdvo y/l oko y ubl hb hk ahbtrl. 7. Hk bdvhk bdvhk prlmhid prlmhidl l ih mobh`l mobh`l ihk gokñb, gokñb, idspor idsporls ls y rhg rhglth lthss ih ko okdbho okdbhoadñ adñb b dbdadok hbh quh shr plr kl mhbls ih ils. 1. Qd hk `ufoilr `ufoilr trhs hmpdhz hmpdhzo o o `ufor, `ufor, hbtlbahs hbtlbahs hk mdhmgr mdhmgrl l shds bl puhih puhih `ufor. `ufor. 9. Qd hk hkhmhbtl hkhmhbtl ubl dbdado, dbdado, hbtlba hbtlbahs hs kls mdhmgrls mdhmgrls auot auotrl rl y adba adbal l tomgdä tomgdäb b ihghb  `ufor. 8. Ihgh Ihgh hmphzo hmphzorr hk `ufoi `ufoilr lr ils ils l hk hk `ufoi `ufoilr lr trhs. trhs. :. Ioios Ioios hstos hstos rhstrd rhstrdaadl aadlbhs bhs,, hk hbtrhboi hbtrhboilr lr ihgh moxdmdzo moxdmdzorr ko aopoadi aopoadioi oi ihjhbsdv ihjhbsdvo o tltok ihk hqudpl dbdadok. Jlrmukh Jlrmukh ub ^H quh oyuih oyuih ok hbtrhboilr hbtrhboilr o hsalfhr hsalfhr o su hqudpl dbdadok.

QLKXADÑB Hk lg`hvl hs ihthrmdbor ko mh`lr shkhaadñb ih `ufoilrhs, quh dbthfrhb ko okdbhoadñb dbdadok. Ih sdhth `ufoilrhs quh thbhmls hkhfdrhmls o kls 8 mh`lrhs, hs ihadr kl hkd`l l bl kl hkd`l, kl quh bls kkhvo o phbsor quh hs ub prlgkhmo gdbordl, sd ko vordogkh vokh ubl, hk  `ufoilr almdhbzo hb ko okdbhoadñb, sd vokh ahrl puhs puhs bl.

 

Sd= Hk `ufoilr d almdhbzo hb ko okdbhoadñb dbdadok. Hk hbtrhboilr ihsho moxdmdzor ko aopoadioi ihk hqudpl, hbtlbahs shfðb kos aopoadioihs ihjhbsdvos ih aoio `ufoilr buhstro jubadñb lg`hvl quhio0  Mox= 1S? + 7S7 + 7S1 + S9 + 1S8 + 1S: + S6 Oclro achaorhmls kos rhstrdaadlbhs. 

^lr kl mhbls auotrl mdhmgrls ihghb shr aopoahs ih `ufor hb ko ihjhbsdvo. Hb hsto rhstrdaadñb dbakudmls o kls `ufoilrhs quh auhbthb alb aopoadioihs ihjhbsdvos. S? + S9 + S8 + S: + S6 ≨ 9

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^lr kl mhbls ils hkhmhbtls ihghb dr o ko ljhbsdvo. Dbakudmls o kls `ufoilrhs alb aopoadioihs aopoadioi hs ljhbsdvos.

 

S? + S1 + S8 + S6 ≨ 7 

 

^lr kl mhbls ub `ufoilr ok ahbtrl. S7 + S9 + S: ≨ ?

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Hk bdvhk prlmhidl ih mobh`l ihk gokñb, ih ko okdbhoadñb dbdadok hbh quh shr plr kl mhbls ih ils. 1S? + 7S7 + 7S1 + S9 + 1S8 + 1S: + 1S6 ≨ 7

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Alml hstomls hkhfdrhmls slkl o 8 `ufoilrhs, idvdidmls hk koil dzqudhril ih ko hauoadñb hb trhs 8 y ihsph`obil bls quhio0  1S? + S7 + 1S1 + 1S9 + 1S8 + S: + 7S6 ≨ ?>

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Hk bdvhk prlmhidl ih mobh`l ih idsporls ih ko okdbhoadñb dbdadok hbh quh shr plr kl mhbls ih ils0  S? + 1S7 + 7S1 + 1S9 + 1S8 + 7S: + 7S6 ≨ ?>

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Hk bdvhk prlmhidl ih mobh`l ih rhglths ih ko okdbhoadñb dbdadok hbh quh shr plr kl mhbls ih ils0  S? + 1S7 1S7 + 7S1 + 1S9 + 1S8 + 7S: + 7S6 7S6

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≨?>

Qd hk `ufoilr trhs hmpdhzo o `ufor, hbtlbahs hk mdhmgrl shds bl puhih `ufor. Hs ihadr, sd S1 vokh ubl, jlrzlsomhbth S: thbirío quh vokhr ahrl.

 

S1 + S:

≩?

 

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Qd hk hkhmhbtl ubl dbdado, hbtlbahs kls mdhmgrls auotrl y adbal tomgdäb ihghb  `ufor.

 

7S? ≩ S9 +S8 

Ihgh hmphzor hk `ufoilr ils l hk `ufoilr trhs. S7+ S1 = ?

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Qlkl plirïb `ufor 8 `ufoilrhs hb ko okdbhoadñb dbdadok. 1S? + 7S7 + 7S1 + S9 + 1S8 + 1S: + S6 = 8  Sd ₫ (>,?)

XQOBIL ^WLFWOMO YLWO

Dbthrprhtoadñb0 Dbdadorïb kls `ufoilrhs ?,1,9,6, iobil ubo slkuadñb ñpmo ih ?>.

 

^WLGKHM ^WLG KHMO O >1 (>: pubtl pubtl)0 )0

Ko hmprhso hmprhso COWI albsdihro albsdihro auotrl dbvhrsdlbhs. dbvhrsdlbhs. Ko dbvhrsdñb ? prlplradlbo ub voklr oatuok bhtl ih Q/?:>>>, ko dbvhrsdñb 7 prlplradlbo ub voklr voklr oatuok oatuok bhtl ih Q/77>>> Q/77>>>,, k o dbvhrsdñb 1 Q/?7>> Q/?7>>>, >, ko dbvhrsdñb 9 Q/3>>> Q/3>>>.. Aoio dbvhrsdñb dbvhr sdñb rhqudhro adhrtl jku`l ih ao`o, ko dbvhrsdñb dbvhrsdñb ? rhqudhrh rhqudhrh Q/8>>>, ko dbvhrsdñb dbvhrsdñb 7 rhqudhr rhq udhrh h Q/6>>> Q/6>>>,, ko 1 rhqudh rhqudhrh rh Q /9>>> /9>>> y ko 9 rhqudh rhqudhrh rh Q/1>>>. Q/1>>>. Qh idsplb idsplbh h ih Q/?9>> Q/?9>>> > poro ko dbvhrsdñb y sh iob kos sdfudhbths rhstrdaadlbhs0 • ^uhih dbvhrtdr auobil auobil muacl hb 7 dbvhrsdlbhs. • Qd dbvdh dbvdhrth rth hb hb 7, hbtlb hbtlbahs ahs tom tomgdäb gdäb ihgh ihgh dbvhrt dbvhrtdr dr hb ?. ?. • Qd dbvdhrth hb 7 bl puhih puhih dbvhrtdr hb 9.

QLKXADÑB Zordogkh Sd0 Xsor ko dbvhrsdñb d Mox P=?:x?+77x7+?7x1+3x9 P=?:x?+77x7+?7x1+3x9 s.o. 8x?+6x +6x7+9x1+1x9;=?9   x?+x7+x1+x9;=7   x7;=x? x7+x9;=? Sd Љ {>,?} XQOBIL ^WLFWOMO KDBIL