Programación Lineal - Modelo

 

JU[LDLXF@LÐG ILGNFI LGCN LG CNGL GLNQ NQÄF LG LGK^ K^P[ P[QL QLFI FI ^GLRNQPLKFK DFG^NIF ANI[QÆG

 

UQJCQFDF@LÐG ILGNFI

 

If jptdlzf`lðg afsfkf ng prjcrfdf`lðg ilgnfi `jrrnspjgkn f sltuf`ljgns rnfins ng ifs qun sn prnngkn lkngtb`fr y rnsjivnr klb`uifkns pfrf fudngtfr if prjku`vlkfk rnspn`j f ijs rn`ursjs (prlg`lpfidngn ijs ildlfkjs y `jsjsjs), fudngtfgkj fsä ijs angnb`ljs.

 

Ijs rnsuifkjs y ni prj`nsj jptdlzf`lðg sn f `jgvlnrng ng ug rnspfikj `ufgtftvj kn ifs knkn`lsljgns rngn ifs sluf`ljgns pifgnfkfs. Kn`lsljgns ng ifs qun snräf ldpjrfgn ngnr ng `ungf klvnrsjs `rlnrljs fkdlglsrftvjs `jdj8 Ijs mn`mjs

If nxpnrlng`lf

If lgtul`lðg

If futjrlkfk

 

ºVuì ns if UQJCQFDF@LÐG ILGNFI: If prjcrfdf`lðg ilgnfi ns ugf tì`gl`f dftndæ`f qun sn uilzf pfrf if sjiu`lðg kn klbnrngtns pjs kn prjaindfs, tfgtj tnðrl`js `jdj præ``js, ng klvnrsfs ærnfs kni `jgj`ldlngtj. Hnsøs y Fgjglj Frrnjif Qlsf ng su ilarj ’Urjcrfdf`lðg Ilgnfi8 ^gf lgrjku``lðg f if jdf kn kn`lsljgns `ufgtftvf—

 

Ni ìxlj ng su fpil`f`lðg f prjaindfs rnfins, sjbst`fkjs y `jdpinhjs ns fvfifkj pjr ugf crfg `fgtkfk kn lgstu`ljgns prjku`jrfs kn alngns y snrvl`ljs ng du`mjs pfäsns kni dugkj. If prjcrfdf`lðg ilgnfi `jgslsn aæsl`fdngn ng if `jgsru``lðg, sjiu`lðg y fgæilsls kni djknij ilgnfi kn ug prjaindf kfkj.

 

Urjcrfdf`lðg Ilgnfi sncøg Slolpnklf….. @jgslsn ng jptdlzfr (dlgldlzfr j dfxldlzfr) ugf ug`lðg ilgnfi, kngjdlgfkf ug`lðg jahntvj, kn fi jrdf qun ifs vfrlfains kn kl`mf ug`lðg nsìg suhnfs f ugf snrln kn rnstrl``ljgns  qun nxprnsfdjs dnklfgn ug slsndf kn lgn`uf`ljgns ilgnfins.

 

Urjcrfdf`lðg Ilgnfi sncøg www.prjcrfdf`lðgilgnf nfii.gnt If Urjcrfdf`lðg Ilgnfi (UI) ns ugf kn ifs prlg`lpfins rfdfs kn if Lgvnstcf`lðg Jpnrftvf. Ng nsf `fncjräf sn `jgslknrfg jkjs fquniijs djknijs kn jptdlzf`lðg kjgkn ifs ug`ljgns qun ij `jdpjgng, ns kn`lr, ug`lðg jahntvj y rnsrl``ljgns, sjg ug`ljgns ilgnfins ng ifs vfrlfains kn kn`lslðg.

 

If prjcrfdf`lðg ilgnfi (UI) ns ugf ì`gl`f dfndæt`f kn jptdlzf`lðg, ns kn`lr, ug dìjkj qun rff kn dfxldlzfr j dlgldlzfr ug jahntvj. Pu lgnrìs prlg`lpfi ns tjdfr kn`lsljgns ðpdfs.

Kr.. C Kr Cul ulii iinr nrd dj D Dfr frttä    gnz gnz Ftlifgj 

 

Nstru`turf aæsl`f k kn nu ug gp prrjaindf kn p prrjcrfdf`lðg iillgnfi ((U UI)

^g prjaindf kn UI `jgsf kn ugf ug`lðg jahnvj (ilgnfi) pjr dfxldlzfr j dlgldlzfr, suhnf f `lnrfs rnstrl``ljgns  ng if jrdf kn lcufikfkns j knslcufikfkns.

 

Nhndpij Cnpnj P.I., dfguf`urf duön`js y rngns kn dfknrf. @fkf duön`j8   Urjku`n ug angnb`lj gnj kn 0 ₩.   Qnqulnrn 1 mjrfs kn r rfafhj fafhj kn f`fafkj.   Qnqulnrn 6 mjrf kn rfafhj kn `frplgnräf `frplgnräf..  @fkf rng8   Urjku`n ug angnb`lj gnj kn 1 ₩.   Qnqulnrn 6 mjrf kn rfafhj kn f`fafkj.   Qnqulnrn 6 mjrf rfafhj kn `frplgnräf.   •

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@fkf sndfgf Cnpnj punkn klspjgnr kn8   [jkj ni dfnrlfi qun gn`nsln.   Pjifdngn 655 mjr mjrfs fs kn f`fafk f`fafkj. j.   Pjifdngn =5 mjrfs kn `frplg `frplgnräf. nräf. [fdalìg8   If kndfgkf kn r rngns ngns punkn snr `u `ufiqulnrf fiqulnrf (slg iädln iädln). ).   If kndfgkf kn duön`js ns `jdj du`mj ;5. •

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Cnpnj qulnrn dfxldlzfr sus angnb`ljs.

º@uægtjs duön`js y `uægtjs trngns knan bfarl`fr:

 

Nstn prjain Nstn prjaindf df ns ug nhndp nhndpij ij tä pl`j kn ug ug prja prjaind indf f kn prjc prjcrf rfdf df`l `lðg ilgn ilgnfi fi (UUI (UUI). ). Rfrlfains kn Kn`lslðg

x 4 g¸ kn duön`js   prjku`lkjs f if   sndfgf y 4 g¸ kn rngns   prjku`lkjs f if   sndfgf

Bug`lðg Jahnvj. Ng `ufiqulnr UUI, if kn`lslðg f jdfr ns `jdj dfxldlzfr (gjrdfidngn ni angnb`lj) j dlgldlzfr (ni `jsn) kn ficugf ug`lðg kn ifs vfrlfains kn kn`lslðg. Nsf ug`lðg f dfxldlzfr j dlgldlzfr sn iifdf ug`lðg jahnvj.

Ni jahntvj kn Cnpnj ns ninclr vfijrns kn x n y pfrf dfxldlzfr 0x + 1y. ^sfrndjs if vfrlfain z pfrf kngjfr ni vfijr kn if ug`lðg jahntvj. If ug`lðg jahntvj kn Cnpnj ns8

Dfx z 4 0x + 1y

Qnstrl``ljgns Pjg knslcufikfkns qun ildlfg ijs pjslains vfijrns kn ifs vfrlfains kn kn`lslðg.

Ng nsn prjaindf ifs rnsrl``ljgns vlngng kfkfs pjr if klspjglalilkfk kn mjrfs kn f`fafkj y `frplgnräf y pjr if kndfgkf kn duön`js. [fdalìg sunin mfanr rnsrl``ljgns kn slcgj j gj gncftvlkfk8 x≮5 y ≮ 5

 

Qnstrl``ljgns @ufgkj  x   n y   `rn`ng, `rn`ng, if ug`lðg jahntvj kn Cnpnj fdalìg `rn`n. Unrj gj punkn `rn`nr lgknbglkfdngn pjrqun, pfrf Cnpnj, ijs vfijrns kn x n y nsæg ildlfkjs pjr ifs slculngns rns rnsrl``ljgns8 p unkng snr usfkfs. Qnstrl``lðg Qnstrl``l ðg 68 gj dæs kn 655 mjrfs kn tndpj kn f`fafkj punkng tndpj kn `frplgnrlf `frplgnrlf punkng snr usfkfs. Qnstrl``lðg Qnstrl``l ðg 18  gj dæs kn =5 mjrfs kn tndpj farl`frsn sn dæs kn ;5 duön`js. Qnstrl``lðg Qnstrl``l ðg 08 ildlf`lðg kn kndfgkf, gj knang farl`fr

Nsfs rns rnsrl``ljgns punkng nxprnsfrsn dfndft`fdngn pjr ifs slculngns knslcufikfkns8 Qnstrl``lðg Qnstrl``lð g 68

1 x + y ≫ 655

Qnstrl``lðg Qnstrl``lð g 18

x +

Qnstrl``lðg Qnstrl``lð g 08

x

y ≫ =5

 ≫ ;5

Fkndæs, ngndjs ifs rnsrl``ljgns kn slcgj8 x ≮ 5 n y ≮ 5  

Bjrduif`lðg dftndætl`f kn UI Rfrlfains kn Kn`lslðg  

x 4 g¸ kn duön`js prjku`lkjs f if sndfgf y 4 g¸ kn rngns prjku`lkjs f if sndfgf

Duön`j

[rng

Angnbl`lj

0

1

 F`fafkj

1

6

≫ 655

@frplgtnräf

6

6

≫ =5

Kndfgkf

Dfx z 4 0x + 1y (ug`lðg jahntvj) 1 x + y ≫ 65 655 5 x + y ≫ =5 x

≫ ;5

(f`fafkj) (`frplgnrlf)

≫ ;5 (kndfgkf duön`js)

 

x  ≮ 5

(rnstrl``lðg kn slcgj)

 

y  ≮ 5

(rnstrl``lðg kn slcgj)

 

Bjrduif`lðg dftndætl`f kni UUI Ufrf ni prjaindf kn Cnpnj, `jdalgfgkj ifs rnsrl``ljgns kn Ufrf slcgj x ≮ 5 n y ≮ 5 `jg if ug`lðg jahntvj y ifs rnsrl``ljgns, ngndjs ni slculngn djknij kn jptdlzf`lðg8  

Dfx z 4 0x + 1y

 

Puhnj f (s.f8)

(ug`lðg jahnvj)

1 x + y ≫ 65 655 5 (rns (rnsrl` rl``lð `lðg g kn f`fafk f`fafkj) j)  

x + y ≫ =5

 

x  ≫ ;5

(r (rns nsr rl` l``l `lðg ðg kn `fr frpl plg gn nrl rlf) f) (r (rns nsr rl` l``l `lðg ðg kn kn kndf dfgk gkf f kn duön duön`j `js) s)

 

x  ≮ 5

(rnsrl``lðg kn slcgj)

 

y  ≮ 5

(rnsrl``lðg kn slcgj)

 

NHNQ@L@LJ 68 If ngsfifkf If gfrfghf `unsf ; pnsjs/olij y tngn 61 crfdjs kn vlfdlgf @ y ug crfdj kn vlfdlgf F. If uvf `unsf 25 pnsjs/olij y tngn 5 crfdjs kn vlfdlgf @ y 12 crfdjs kn vlfdlgf F. If zfgfmjrlf `unsf 61 pnsjs/olij y tngn 0 crfdjs kn vlfdlgf @ y 65 crfdjs kn vlfdlgf F. If in`mucf `unsf ; pnsjs/olij y tngn 1 ugf crfdjs kn vlfdlgf @ ypnrsjgfs ; crfdjs qun kn vlfdlgf F. ng jfi Pn knsnf prnpfrfr ngsfifkf pfrf 65 `jgngcf `ufgkj dngjs 65 crfdjs kn vlfdlgf @ y 61 crfdjs kn vlfdlgf F.

 

NHNQ@L@LJ 18 If bnil`lkfk kn Unpn

 

NHNQ@L@LJ 08 @f @fsfs kn d du uön`fs ^gf ndprnsf, nspn`lfilzfkf ng if farl`f`lðg kn djalilfrlj pfrf `fsfs kn duön`fs, prjku`n `lnrj tpj kn dlgldnsfs y dlglsliifs qun vngkn f 1555 uglkfkns djgnfrlfs (u.d.) 0555 u.d. pjr `fkf fr`uij, rnspn`tvfdngn. Knsnf sfanr `uægfs uglkfkns kn `fkf fr`uij knan farl`fr klfrlfdngn ug jpnrfrlj pfrf dfxldlzfrr ijs lgcrnsjs, nglngkj ifs sslculngns dfxldlzf lculngns rnsrl`` rnsrl``ljgns8 ljgns8 Ni gødnrj jfi kn uglkfkns kn ijs kjs tpjs gj pjkræ nx`nknr kn `ufrj pjr käf y jpnrfrlj. @fkf dlgldnsf rnqulnrn kjs mjrfs pfrf su farl`f`lðg? `fkf dlglsliif, rns mjrfs. If hjrgfkf ifajrfi dæxldf ns kn klnz mjrfs. Ni dfnrlfi utilzfkj ng `fkf dlgldnsf `unsf ;55 u.d. Ni utilzfkj ng `fkf dlglsliif `unsf 155 u.d. @fkf jpnrfrlj klspjgn kn 6155 u.d. klfrlfs pfrf dfnrlfi. Uifgnfr y rnsjivnr ni fgnrljr prjaindf `jdj ug djknij kn prjcrfdf`lðg ilgnfi.