Ejercicios Investigación de Operaciones

 

_riaj`gn >= 1?68?>>0? p`sis. Xupikf`kei qu`  tiei ji qu` s` prieuh` s` v`ke`. _riaj`gn 1= >668???8 

Pkn bîarfhn e` hnrrih`rçns e` nutigøvfj`s A`rjfkn y nutigøvfj`s Hupæ tf`k` eis e`pnrtng`ktis. @k `j e`pnrtng`kti  N, pnrn lnh`r jn hnrrih`rçn e` uk Hupæ, s` fkvf`rt`k 6 eçns-ip`rnrfi, pnrn bnarfhnr jn e` uk A`rjfkn s` pr`hfsnk 5 eçns-   ip`rnrfi. @k `j e`pnrtng`kti A s` fkvf`rt`k huntri eçns ip`rnrfi tnkti `k hnrrih`rçns e` Hupæ y tr`s eçns ip`rnrfi   pnrn hnrrih`rçns e` A`rjfkn. _ir jfgftnhfik`s e` gnki e` iarn y gnqufknrfn, `j e`pnrtng`kti N efspik` e` 1153 

Gnku`j, c`r`kt` e` Gf Qnkhlfti , pripirhfikn nja`rcu`s pnrn p`rris. @j njfg`kti pnrn p`rris Gnshitn B`jfz   s`  lnh` g`zhjnkei eis prieuhtis e` siyn pnrn iat`k`r ukn "ef`tn pnrn p`rris af`k anjnkh`nen". @k jn Unajn s` enk jis  entis pnrn jis eis prieuhtis. Xf Gnku`j quf`r` ns`curnrs` e` qu` sus p`rris r`hfank nj g`kis 3 dfjicrngis e`  prit`çkns y 1 dfjicrngi e` crnsn efnrfng`kt`, ¹huîj s`rçn jn g`zhjn e`j histi gçkfgi e` jis eis njfg`ktis n jfg`ktis pnrn p`rri9 ‚

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_rieuhti e` siyn  > 

Histi pir dfjicrngi 

_rit`çkn (%) 

Crnsns (%) 

$1>.18

5?

>0

1 

$>1.5>

>?

0

 

_riaj`gn _ria j`gn 2= 1?68? 1?68?>?< >?0 r`njfznr ukn jjngnen t`j`bøkfhn eurnkt` `j eçn,  y $8? r`njfznr ukn jjngnen t`j`bøkfhn eurnkt` jn kihl` (e`afei n gnyir`s histis jnairnj`s). @stis entis s` gu`strnk `k jn tnajn fkb`rfir. X` pu`e`k r`njfznr n ji gîs uk 8?% e` `stns jjngnens `k jn kihl`, pir efspik`r e` uk kýg`ri  jfgftnei e` `gpj`neis. ¹Huîktns jjngnens eurnkt` `j eçn y huîktns eurnkt` jn kihl`, e`a`k r`njfznrs` pnrn gfkfgfznr   jis histis pnrn higpj`tnr jn `khu`stn9 _`rsikn qu` hikt`stn  @stuefnkt`s ligar`s  @stuefnkt`s gum`r`s  _ner`s e` bngfjfn  Ki hikt`stnk  

% e` jjngnens efurkns 

% e` jjngnens kihturkns 

1? 50 0 8?

1? >? 3? >?

_riaj`gn _ria j`gn 3= 1?68? 1?68?116 116 

Jns r`strfhhfik`s p`squ`rns fgpu`stns pir jn X@GNQKNU iajfcnk n hf`rtn `gpr`sn n p`shnr higi gîxfgi 18,???  tik`jnens e` hngnrøk y 81,??? tik`jnens e` ntýk, ne`gîs, `k titnj, jns hnpturns e` `stns eis `sp`hf`s ki pu`e`k  pnsnr e` jns 80,??? tik`jnens. Xf `j pr`hfi e`j hngnrøk `s e` 61 p`sis `j dfji y `j pr`hfi e`j ntýk `s e` >>? p`sis `j  dfji, ¹quæ hnktfene`s e`a` p`shnr pnrn iat`k`r `j gîxfgi a`k`bfhfi9 _riaj`gn _ria j`gn >2 >>2 

Pk v`ke`eir e` gnrfshis k`h`sftn higi gçkfgi 15 hnmns e` tfjnpfn, 81 hnmns e` hngnrøk y >2 e` pujpi. Eis  gnyirfstns, G`xih`nk y Fkt`rgnr Gæxfhi, s` ibr`h`k nj lfp`rg`rhnei pnrn sntfsbnh`r sus k`h`sfene`s, p`ri søji  v`ke`k efhli gnrfshi `k hikt`k`eir`s higpj`tis. @j gnyirfstn G`xih`nk `kvçn `k hnen hikt`k`eir 2 hnmns e`   tfjnpfn, < e` hngnrøk y 5 e` pujpi. _ir su pnrt`, Fkt`rgnr Gæxfhi `kvçn `k hnen hikt`k`eir 1 y 2 hnmns  r`sp`htfvng`kt`. Hnen hikt`k`eir qu` sugfkfstrn G`xih`nk hu`stn $81,???, gf`ktrns qu` jis e`j gnyirfstn   Fkt`rgnr Gæxfhi hu`stnk $58,??? hnen uki. ¹Huîktis hikt`k`eir`s e`a`k p`efr `j lfp`rg`rhnei lfp`rg`rhnei n hnen gnyirfstn  pnrn sntfsbnh`r sus k`h`sfene`s gçkfgns hik `j g`kir hist` pisfaj`9 _riaj`gn _ria j`gn 6= >368? >368?>31 >31 

Pkn pjnktn e` prieuhtis e` jfgpf`zn prieuh` eis prieuhtis (e`t`rc`kt`s y mnaik`s), `k jn gfsgn jçk`n e` `ksngaj`.  Jns sik jçk`n e` `k `ksngaj` hikstn e` tr`s e`pnrtng`ktis. Jis tf`gpis e` `ksngajnm` `k jis e`pnrtng`kti e`pnrtng`ktis eneis   jn sfcuf`kt` tnajn. E`pnrtng`kti 

E`t`rc`kt`s  (ukfene`s/gfkuti)  

Mnaik`s  (ukfene`s/gfkuti)  

Ip`rnrfis  @khnrcneis e`j tnjj`r  _`rsiknj tæhkfhi `sp`hfnjfzn `sp`hfnjfznei ei 

>? 8 5

>1 3 2

Hnen e`pnrtng`kti tf`k` efspikfaj` jns >1 lirns e` trnanmi efnrfi. Xfk `ganrci, jis e`pnrtng`ktis r`quf`r`k  gnkt`kfgf`kti efnrfi, qu` utfjfznk `j >?%, 6% y 0% e`j tf`gpi efspikfaj` pnrn hnen e`pnrtng`kti efnrfng`kt`. Jn  pjnktn e`s`n sna`r jns ukfene`s s`gnknj`s (s` trnanmn 0 eçns n jn s`gnkn) qu` s` `ksngajnrnk n bfk e` gfkfgfznr jn  sugn e` tf`gpis ki ihupneis (ihfisis) `k jis tr`s e`pnrtng`ktis.

 

_riaj`gn _ria j`gn >?= 1?68? 1?68??66 ?66 

Jn `gpr`sn Jnjn `jnairn yicurt y mucis n ans` e` br`sn y eurnzki, `stn `gpr`sn higprn su gnt`rfn prfgn nj pr`hfi  e` $10 pir dfjicrngi e` br`sn y $1? pir dfjicrngi e` eurnzki, jns hnktfene`s gîxfgns qu` pu`e` higprnr `s e` 5.0  tik`jnens e` gnkci y 2.8 tik`jnens e` eurnzki. @j g`rhnei e` v`ktn e` yicurt `s e` 2?,??? 2?, ??? ait`jjns higi gîxfgi y pnrn muci e` 6?,??? ait`jjns, `j pr`hfi e` v`ktn  e`j yicurt y e` muci `s e` $1? $1 ? y $10 pir hnen ait`jjn r`sp`htfvng`kt`4 `k jn sfcuf`kt` tnajn s` gu`strnk ji utfjfznei  pnrn `jnairnr yicurt y muci. Vicurt Br`sn  Eurnzki 

Mucis 

>.0 dc/ait`jjn >.1 dc/ait`jjn

>.< dc/ait`jjn >.> dc/ait`jjn

_riaj`gn >>= 1?68?>?2 

Pk l`rr`ri hik 6? Dc. e` nh`ri y >?? Dc. e` njugfkfi quf`r` lnh`r afhfhj`tns e` hfhjfsgi y e` giktnþn qu` quf`r`  v`ke`r, r`sp`htfvng`kt` n 1= 1?68?>?> 

Pk nutiaýs qu` lnh` `j r`hirrfei Hu`rknvnhn-Nhnpujhi, ibr`h` nsf`ktis `m`hutfvis nj pr`hfi e` 232 p`sis y nsf`ktis  e` prfg`rn nj pr`hfi e` 530 p`sis. N jis e` nsf`ktis nsf `ktis `m`hutfvis s` j`s e`mn jj`vnr 1? Dc e` p`si y n jis e` nsf`ktis e`  prfg`rn >? Dc. Xf `j nutiaýs tf`k` 50 nsf`ktis y negft` uk `qufpnm` e` lnstn 1,0?? Dc. ¹Huîj ln e` s`r jn ib`rtn e`   nsf`ktis e` jn higpnþçn pnrn hnen tfpi e` pnsnm`ris, hik jn bfknjfene e` iptfgfznr `j a`k`bfhfi9 Ne`gîs, e`a`  hiksfe`rnrs` qu`, pir pijçtfhns e` jn `gpr`sn, e`a`k ibr`h`rs` høgi gçkfgi 1? nsf`ktis e` prfg`rn. _riaj`gn >8= 1?68?18 1?68?188 8 

Pk hig`rhfnkt` e` brutns k`h`sftn 8? hnmns e` knrnkmns, 10 e` pjîtnkis y 1? e` gnkznkns. Eis gnyirfstns `stîk `k  hikefhfik`s e` sntfsbnh`r sus k`h`sfene`s, p`ri siji v`ke`k jn brutn `k hikt`k`eir`s higpj`tis. @j gnyirfstn  Nrcfnansti  `kvçn `k hnen hikt`k`eir >? hnmns e` knrnkmns, >? e` pjîtnkis y 0 e` gnkznkns. @j ‚

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gnyirfstn Brutis  hik Xnair n Gæxfhi  `kvçn `k hnen hikt`k`eir 0 hnmns e` knrnkmns, 0 e` pjîtnkis y >? e` gnkznkns. Xnaf`kei qu`  `j gnyirfstn Nrcfnansti  s` `khu`ktrn n 1>? 

Pkn `gpr`sn e` hikb`hhfik`s pu`e` prieuhfr >0 

K`stjæ, prieuh` y efstrfauy` eis eis tfpis e` hnbæ n jis ssup`rg`rhneis up`rg`rhneis e`j pnçs= hnb`fknei y e`shnb`fknei. _nrn `st` g`s  K`stjæ tf`k` 20? tik`jnens e` crnki e` hnbæ `k fkv`ktnrfi y tf`k` pricrngnens lnstn 3? lirns e` tf`gpi e`  prih`sngf`kti pnrn `j tistnei. Hnen tik`jnen e` hnbæ hnb`fknei k`h`sftn eis tik`jnens e` crnki, huntri lirns e`  tistnei y prieuh` ukn cnknkhfn e` $>6,???. Hnen tik`jnen e` hnbæ e`shnb`fknei k`h`sftn ukn y g`efn tik`jnen e`   crnki, p`ri k`h`sftn s`fs lirns e` tistnei y prieuh` ukn cnknkhfn e` $18,???. _jnkt`` uk gie`ji e` pricrngnhføk  jfk`nj qu` j` p`rgftn n K`stjæ pjnk`nr pjn k`nr su prieuhhføk pnrn `st` g`s. _riaj`gn >?? 

Pk cnkne`ri pis`` 50? r`s`s qu` hiksug`k 50 dc e` higfen `sp`hfnj tieis jis eçns. @j njfg`kti s` pr`pnrn higi  ukn g`zhjn e` gnçz y sirci hik jns sfcuf`kt`s higpisfhfik`s= higpisfhfik`s= Njfg`kti 

Hnjhfi 

_rit`çkn 

Bfarn 

Histi  ($/dc) 

Gnçz  Xirci 

?.?1 ?.?8

?.>1 ?.16 

Pkn hnrpfkt`rçn bnarfhn eis tfpis e` hngns. @j ýkfhi r`hursi `shnsi qu` s` k`h`sftn pnrn prieuhfr jns hngns `s jn  gnki e` iarn. Nhtunjg`kt` jn hnrpfkt`rçn tf`k` eis trnanmneir`s. Misæ Nja`rti `stî efspu`sti n trnanmnr lnstn 515 

Pk hig`rhfnkt` nhue` n jn h`ktrnj e` nanstis n higprnr bjir`s hik 80?,??? p`sis. J` ibr`h`k eis tfpis e` bjir`s=  risns n 30? p`sis `j Dc y jis tujfpnk`s n 6?? p`sis `j Dc. Xnaf`kei qu` søji efspik` e` su hngfik`tn hik `spnhfi  pnrn trnkspirtnr >,1?? Dc. e` bjir`s higi gîxfgi y qu` pf`ksn v`ke`r `j Dc. e` risns n >,1?? p`sis. y `j Dc. e`   tujfpnk`s n >0?? p`sis. pjnkt`` uk gie`ji e` pricrngnhføk jfk`nj qu` p`rgftn r`sijv`r jn sftunhføk nkt`rfir. _riaj`gn 11= 1?68?>>6 

Pkn higpnþçn tf`k` eis crneis e` fksp`htir`s=  mukfir y s`kfir , qu` sik nsfckneis nj hiktrij e` hnjfene. X` r`quf`r`  fksp`hhfiknr n ji gîxfgi 56?? pf`zns pir eçn (< lirns). @j fksp`htir  mukfir r`vfsn pf`zns n v`jihfene e` 86 pf`zns pir  lirn hik ukn `xnhtftue e`j 6?%. Jis s`kfirs r`vfsnk n v`jihfene e` 10 pf`zns pir lirn hik ukn `xnhtftue e`j 66%. @j snjnrfi e`j fksp`htir  mukfir `s e` $18? /lirn, y `j s`kfir e` $50?/lirn. Hnen v`z qu` s` prieuh` uk `rrir, `j  hist` n  jn higpnþçn `s e` $0?. Jn higpnþçn tf`k` < fksp`htir`s  mukfir y >? s`kfir . E`t`rgfknr jn nsfcknhføk øptfgn e`  fksp`htir`s qu` gfkfgfh`k `j hist` titnj e` fksp`hhføk. _riaj`gn _ria j`gn 18= >668? >668??36 ?36

J@CI nrgn tr`s mucu`t`s= @stnhføk @spnhfnj, Jngairclfkf y Antgnk, hik tr`s ip`rnhfik`s. Jis jçgft`s efnrfis e` tf`gpi efspikfaj` pnrn jns tr`s ip`rnhfik`s sik 01?, 23? y 0>? gfkutis, r`sp`htfvng`kt`, y jns utfjfene`s pir @stnhføk @spnhfnj, Jngairclfkf y Antgnk sik $12, $81 y $50, r`sp`htfvng`kt`. Jis tf`gpis e` nrgnei pir @stnhføk @spnhfnj, `k jns tr`s ip`rnhfik`s sik 2, >5 y 3 gfkutis, r`sp`htfvng`kt`. Jis tf`gpis r`sp`htfvis pir Jngairclfkf y pir Antgnk sik (?, >8) y (0, ( 0, 6, >1) gfkutis. _riaj`gn 15= 1?68?>>3

Pkn p`qu`þn `gpr`sn v`ke` eis prieuhtis, e`kigfkneis prieuhti > y prieuhti 1. Hnen tik`jnen e` prieuhti > hiksug` 52 lirns e` trnanmi, y ukn e`j _rieuhti 1 hiksug` 81 lirns e` trnanmi. Jn `gpr`sn tf`k` uk

 

gîxfgi e` 5,6?? lirns e` trnanmi pnrn `j p`rçiei hiksfe`rnei. @k hunkti n jns lirns e` gîqufkn, hnen tik`jnen e` prieuhtis > y 1 hiksug` 6 y >0 lirns e` gîqufkn, r`sp`htfvng`kt`. Lny >83? lirns e` gîqufkn efspikfaj`s. Hnen tik`jnen e` prieuhti > prieuh` 58 PXE e` a`k`bfhfi, gf`ktrns qu` `j prieuhti 1 rfke` 60 PXE pir hnen tik`jnen v`kefen. _ir rnzik`s tæhkfhns, jn j n `gpr`sn e`a` prieuhfr uk gçkfgi e` >18 tik`jnens `k titnj `ktr` ngais prieuhtis. K`h`sftngis sna`r huîktns tik`jnens e` prieuhti > y 1 s` e`a`k prieuhfr pnrn gnxfgfznr `j a`k`bfhfi titnj. _riaj`gn 10= 1?68?> 1?68?>>1 >1

Ur`s prieuhtis sik bnarfhneis `k ukn gîqufkn. @j tf`gpi e` pr`pnrnhføk e` hnen prieuhti `s e` >2, 1? y 15 gfkutis r`sp`htfvng`kt`, y `j tf`gpi e` prih`si e` 5, 0 y 2 gfkutis. @j a`k`bfhfi npirtnei pir hnen prieuhti `s r`sp`htfvng`kt` e` 18, 85 y 50 `uris. X` efspik` e` 185 gfkutis e` gîqufkn y 850 pnrn jn pr`pnrnhføk e` jn gfsgn. E`t`rgfk` `j kýg`ri øptfgi e` ukfene`s n bnarfhnr e` hnen nrtçhuji. _riaj`gn 12= 1?68?1 1?68?18? 8?

Pkn `gpr`sn `ksngajn uk prieuhti qu` hikstn e` tr`s pf`zns e`kigfknens NN, AA, y HH. Jns pf`zns NN y AA jns bnarfhn jn pripfn `gpr`sn, gf`ktrns qu` jns pf`zns HH jns higprn n itri bnarfhnkt`. Jis tf`gpis e` prih`si, `k lirns, r`qu`rfeis pir hnen pf`zn `k hnen uki e` jis prih`sis vf`k`k eneis `k jn tnajn sfcuf`kt`=

NN AA

_rih`si > 1 >.0

_rih`si 1 >.0

_rih`si 8 1.0 >.0

_rih`si 5

_rih`si 0

>.0

>.0

Jn `gpr`sn efspik` e` 8? gîqufkns qu` pu`e`k r`njfznr `j prih`si >, >> `j prih`si 1, 81 `j prih`si 8, >8 `j prih`si 5 y >> `j prih`si 0. Hnen gîqufkn trnanmn uk gîxfgi e` s`fs eçns hnen s`gnkn n rnzøk e` hfkhu`ktn y eis s`gnkns nj nþi, `k mirknens jnairnaj`s e` < lirns efnrfns. E`t`rgfk` `j kýg`ri gîxfgi e` hikmuktis `ksngajneis qu` pu`e` prieuhfr.