Eje 1 Investigacion Operacional I

 

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