Eje 1 Investigacion Operacional I
October 14, 2022 | Author: Anonymous | Category: N/A
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9
GDG 9
Z@IF^GIECGF^L NG Z]LM@GEIX S XL@WHCLF ZL] EG^LNL A]IBCHL
DGCXXLF IWAWX^L I]IALFGX L]DWG@I
BWFNIHCLF WFCRG]XC^I]CI NG@ I]GI IFNCFI
BIHW@^IN NG CFAGFCG]CI
Z]LA]IEI CFAGFCG]CI CFNWX^]CI@ RC]^WI@
CFRGX^CAIHCLF LZG]IHCLFI@ C G@XS HOIZI]]L OG]FIFNGT
LH^WM]G =:=9
Ngnchitlrci
=
GDG 9
Gstg ^rimidl gs Ngnch Ngnchinl inl Zrcegriegf Zrcegriegftg tg i Ncls, `ugal i fugstris fugstris Biec`cis Biec`cis plr g` Iplyl qug fls mrcfnirlf piri `i ]gi`czihcøf ng gstg ^rimidl, nifnl `ls egdlrgs hlfsgdls y lrcgftifnl slmrg g` ibghtl y Ielr qug oiy qug tgfgr i `i Gnuhihcøf.
8
GDG 9
Iaringhcecgftls
Arihcis i `i Wfcvgrscnin Érgi Ifncfi, i `ls Zrlbgslrgs plr Mrcfnirfls g` iplyl y Gfsgùifzis piri blreirfls hlel Zgrslfis Zrlbgsclfi`gs y piri Iplrtir i `i Xlhcgnin.
>
GDG 9
Gdgrhchcl F.´ 9.
Wfi bémrchi g`imlri nls prlnuhtls ncbgrgftgs Z9 y Z= y utc`czi trgs eéqucfis ncbgrgftgs4 E9, E=, E8. Iemls prlnuhtls rgqucgrgf g` usl, scf ceplrtir g` lrngf, ng `is trgs eéqucfis. Hini ufcnin ng` prlnuhtl Z9 rgqucgrg ufi olri gf hini ufi ng `is eéqucfis. Hini ufcnin ng` prlnuhtl Z= rgqucgrg ufi olri gf `i eéqucfi E9 y nls olris gf `i eéqucfi E=. @is ncsplfcmc`cnings egfsui`gs ng `is eéqucfis E9, E=, E8 slf >::, 7?: y 8:: olris, rgspghtcviegftg. @i eitgrci prcei fghgsirci piri `i bimrchihcøf ng `ls prlnuhtls gs euy béhc` ng lmtgfgr y sg hlfscaug gf hiftcnings tif arifngs qug sg pugngf suplfgr c`cectinis (Mizirii,9333). Ngspuãs ng oihgr g` hé`hu`l ng tlnls `ls aistls fghgsircls piri `i bimrchihcøf, pum`chcnin, ncstrcmuhcøf, ncstrc muhcøf, hlegrhc hlegrhci`czi i`czihcøf hcøf y tgfcgfnl tgfcgfnl gf hugfti g` prghcl ng vgfti, sg lmtcgfg qug g` mgfgbchcl plr hini ufcnin ng` prlnuhtl Z9 gs $9:::. Ziri g` prlnuhtl Z= g` mgfgbchcl ufctircl gs ng $9>::. I` gstuncir `i ngeifni ihtui` piri `ls prlnuhtls, `i hlepiùåi pcgfsi qug pugng vgfngr tlni su prlnuhhcøf. G` agrgftg ngsgi lraifczir su prlnuhhcøf piri qug gsti sgi øptcei (Mizirii, 9333) 9 333) ]gspugsti4
Xg ngbcfg `i Rircim`g ng` prlm`gei, sg ngmg tgfgr g` hlflhcecgftl ng` fôegrl ng ufcnings ng hini prlnuhtl qug oiy qug bimrchir egfsui`egftg.
7
GDG 9
Xgif4 x 95 ¼¼ Fôegrl ng ufcnings ng` prlnuhtl Z9 qug ngmgf sgr bimrchinis hini egs. x =5¼¼ Fôegrl ng ufcnings ng` prlnuhtl Z= qug ngmgf sgr bimrchinis hini egs.
Si gstéf ngbcfcnis `is vircim`gs, sg gxprgsi `i bufhcøf lmdgtcvl l ghlføechi utc`czifnl `is scaucgftgs vircim`gs. Eixceczir z 59::: x 9 + 9>:: x=
Xg gxprgsi `i ngscaui`nin x 9+ x= ≮ >::
Ninl gstl sg ni `i rgstrchhcøf qug sg pugng gxprgsir4 x 9+ = x = ≮ 7?:
Bcfi`egftg gf `i E 8 sg tcgfg4 _ 9 ≮ 8::
@is Rircim`gs x 9 , x = fl pugngf tleir vi`lrgs fgaitcvls, plrqug fl tcgfg sgftcnl oim`ir, ng prlnuhg ‘ 7 ufcnings ng` prlnuhtl Z=; gftlfhgs4 x 9 ≧ : x = ≧ :
2
GDG 9
Xg ]gsug`vg g` prlm`gei lmtgfcgfnl hlel prlnuhhcøf øptcei ng 17.? y ng =>3.= tleifnl hlel rgsu`tinl øptcel x 95 12, x = 5 =>3. ‘ Xg ngmg tgfgr gf hugfti `is vircim`gs ngmgf sgr gftgris y g` elng`l bcfi` ng` prlm`gei gs `i scaucgftg4 Eix z 59::: x 9 + 9>:: x =
Xudgtl i x 9+ x= ≮ >:: x 9+ = x = ≮ 7?: x 9 ≮ 8:: x ≧ :
Xg oihg eés hlepihti gsti prgsgftihcøf scf pgrngr `i prghcscøf, lectcgfnl ng iquå gf ing`iftg g` sudgtl ‐i― l i vghgs ‐ti` qug―, sg ecfceczi ufi bufhcøf l vi`lr z qug ngpgfng ng x 9 , … , x f , nlfng ingeés, x gsti sudgtl i `is rgstrchhclfgs qug scaugf i `i bufhcøf lmdgtcvl.
Gdgrhchcl F. ´ =.
Wf bimrchiftg ng ihgrl prlnuhg huitrl tieiùls ng vcais C4 pgqugùi, egncifi, `irai y gxtri `irai. Gstis vcais sg pugngf prlnuhcr gf hui`qucgri ng trgs tcpls ng eéqucfis4 I, M y H. I hlftcfuihcøf, sg cfnchif `is `lfactungs (gf pcgs) ng `is vcais C qug pugngf prlnuhcr `is eéqucfis plr olri.
1
GDG 9
RCAI Zgqugùi c 5 9 Egncifi c 5 = @irai c 5 8 Gxtri @irai c 5 >
Eéqucfi
I; d 5 9 8::
M; d 5 = 2::
==7::: 9::
>8:7:: =::
Xuplfai qug hini eéqucfi sg pugng usir oisti 7: olris plr sgeifi y qug `ls hlstls ng lpgrihcøf plr olri ng gstis trgs eéqucfis slf4 $8:, $7: y $?: rgspghtcviegftg. Ingeés, suplfai qug sgeifi`egftg sg rgqucgrgf 9:.:::, ?.:::, 2.::: y 2.::: pcgs ng `ls ncstcftls tieiùls ng `is vcais C. Blreu`g g` prlm`gei ng prlarieihcøf ng eéqucfis hlel uf prlariei `cfgi`.
]gspugsti4 Bufhcøf Lmdgtcvl4 Ecfceczir `ls hlstls ng `i prlnuhhcøf ng `is vcais agfgrinis
sgeifi`egftg. Rircim`gs ng nghcscøf4 T4 hlstl ng prlnuhhcøf ng Rcais agfgrinis sgeifi`egftg. x c d
4 Fôegrl ng olris rgqugrcnis piri prlnuhcr `i vcai ng tieiùl c gf `i eéqucfi d
nlfng…
H; d 5 ?:: 12:::: 8::
?
GDG 9
c 5 9, =,8, > (tieiùl ng vcai ng egflr i eiylr ng ihugrnl i `i tim`i iftgrclr); d 5 9, =, 8 (^cpl ng eéqucfi I, M, H)
Bufhcøf Lmdgtcvl4 x 9=+ x== + x 8=+ x >= ) + ?: ( x 98 + x =8+ x 88 + x >8) ecf z 58: ( x x 99+ x =9+ x 89+ x >9) + 7: ( x ]gstrchhclfgs4 Eéqucfi I4 x 99+ x =9+ x 89 + x >9 ≮ 7: Eéqucfi M4 x 9=+ x ==+ x8= + x >= ≮ 7: Eéqucfi H4 x 98+ x =8 + x 88+ x >8 ≮ 7:
Zrlnuhhcøf ng Rcai ng tieiùl c plr sgeifi4 c 59 ; 8:: x 99+ 2:: x 9=+ ?:: x 98 ≧ 9:.::: c 5= ; =7: x=9 + 2:: x ==+ ?:: x =8 ≧ ?.::: c 58 ; =:: x 89+ 87: x 8=+ 2:: x 88 ≧ 2.::: c 5 > ; =7: x >9+ >:: x >= + 1:: x >8 ≧ 2.:::
Zrlariei @cfgi` x 9=+ x== + x 8=+ x >= ) + ?: ( x 98 + x =8+ x 88 + x >8 ) x 99 + x =9+ x 89 + x >9) + 7: ( x ecf z 5 8: ( x
Xudgtl i4
x 99+ x =9+ x 89+ x >9 ≮ 7:
3
GDG 9
x 9=+ x ==+ x8= + x >= ≮ 7: x 98 + x =8 + x 88+ x >8 ≮ 7: 8:: x 99+ 2:: x9= + ?:: x 98 ≧ 9:.::: =7: x =9+ 2:: x == + ?:: x =8 ≧ ?.::: =:: x 89+ 87: x 8=+ 2:: x 88 ≧ 2.:::
x 99 , x 9= , x 98 , x =9 x == x =8 x 89 x 8= x 88 x >9 x >= x >8 ≧ :
Gdgrhchcl F. ´ 8.
Wfi eudgr hleprø trgs h`isgs ncbgrgftgs ng ihhclfgs plr $=:,:::. Wfi ng g``is piai uf 2% ifui` ng cftgrgsgs, ltri piai uf 1%, y `i ltri uf ?% ifui`. I` bcfi` ng` prcegr iùl, `i suei ng `ls cftgrgsgs cftgr gsgs ng `is ihhclf ihhclfgs gs i` 2% y i` 1% gs ng $3>:, y `i suei ng `ls cftgrgsgs ng `is ihhclfgs i` 2% y i` ?% gs ng $1=:. ¼Huéftl cfvcrtcø gf hini ufi ng `is ihhclfgs< (Mizirii, 9333). ]gspugsti4 :.:1 x + :.::2 y 58>: :.:2 x + :.:? y 51=: :.:1 x + :.:2 y 58>: x
(-:.:?)
9:
GDG 9
:.:2 x + :.:? y 51=: x ( :.:2 )
∝:.::72 x ∝:.::>? y 5∝=1.= :.::82 x + :.::>? y 5 >8.=
∝:.::=: x 592 _ 5
92 :.::=:
5?,:::
:.:1 ( ?::: ) + :.:2 y 58>:
72: + :.:2 58>:
S 5
=:: :.:2
5 8,888
Gf g` 1 % cfvcrtcø ?,::: y gf g` 2 % cfvcrtcgrlf 8,888.
]gsl`vgr plr g` eãtlnl arébchl4 Gdgrhchcl F. º> Eix z4 7 x 9+7 x = s.i.4 > x 9+ = x =≮ 92 ? x 9+9= x =≮ >? x 9, x =≧ :
99
GDG 9
Gdgrhchcl F. ´ 7. Eix z4 8:: x 9+9::x\= x = X.i.4>: x 9+? x = ≮ ?:: 9: x 9+7 x = ≮ 8=: x = ≮ 2: x 9, x = ≧ :
Aribchifnl `is 8 rgstrchhclfgs ng` prlm`gei sg lmtcgfgf plr supugstl ufi rgacøf bihtcm`g nlfng sg gfhugftri `i sl`uhcøf øptcei4
9=
GDG 9
Xg cngftcbchi `i sl`uhcøf øptcei sg gvi`ôi tlnls `ls puftls ng cftgrsghhcøf y fls qugniels hlf `i T eés arifng y qug sg gfhugftri gf `i rgacøf bihtcm`g ngmcnl i qug gs uf prlm`gei ng eixceczihcøf.
Zuftl
Hllrngfini _ ( x9 )
Hllrngfini S ( x = )
Ri`lr ng `i bufhcøf lmdgtcvl (T)
98
GDG 9
: I M H N G B A O
: : =: 9= ? : 8= = :
: 9:: : >: 2: 2> : 2: 2:
@i Xl`uhcøf øptcei ng gstg prlm`gei gs4 x 959= , x =5¼ >: nlfng T 5 12:: Xg Xustctuyg `ls nitls gf `is rgstrchhclfgs qug sg tcgfg4 >: (9=) + ? (>:) 5 ?:: ≮ ?:: 9: x 9 + 7 x = 5 8=: ≮ 8=: x = 5 >: ≮ 2:
Gdgrhchcl F. ´ 2. Ecf z4 9::x + 2:x
s.i
∝9 >
x 9+ x = ≧ :
x 9 x = ≧ 9::
: 9:::: 2::: 12:: ?>:: 2>:: 32:: 22:: 2:::
9>
GDG 9
∝ x 9 x = ≮ 97: 9: x 9+ 9= x = ≮ 88:: 8: x 9+ 2 x = ≮ 2:::
x 9 x = ≧ :
s.i
∝9 >
x 9+ x = ≧ :
x 9 x = ≧ 9::
∝ x 9 x = ≮ 97: 9: x 9+ 9= x = ≮ 88:: 8: x 9+ 2 x = ≮ 2:::
x 9 x = ≧ :
97
GDG 9
]gbgrgfhcis
ottps4//www.ihrcpfihclfi`.lra/ceplrtifhci-ng-`i-tghfl`laci-gf-`is-pyegs-y-geprgsis-gfhrghcecgftl/ ottps4//www.eistgrcfnustrci>:.hle/vgftidis-ngsvgftidis-cfnustrci->-:/ ottps4//www.vcibcrei.nl/mirrgris-pyegs-cfnustrci->-:/
92
GDG 9
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