Page 350 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

VED1
E L-LOVELY-H math27-1 IInd 6-8-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

noEPk;soh dk rfDs

B'N d' uo (variables), z d/ cbB (function) j'D, sK z dk w[Zb T[; ;w/A tZX s'A tZX j't/rk, id'A T[;
fpzd{ Bkb ehsh rJh fe;h th rsh d[nkok z dk w[Zb xZN j' ikt/. z dk w[Zb T[; ;w/A fBT{Bsw
j[zdk j?, id'A fe fe;h th rsh Bkb z dk w[Zb tZX j' ikt/. id'A fBors d/ nkeko d/ Bkb gqsh
fJekJh bkrs ns/ ehws ftZu gfotosB j't/, sK ;wZf;nkt o/yh BjhA j[zdh ns/ i/eo fBors
d/ Bkb T[jBK ftZu gfotosB BjhA j[zdk, sK ;wZf;nk o/yh j[zdh j?. fJ; soQK gq'rokfwzr dh
gfoGkPk fJ; soQK fdZsh ik ;edh j? fe fJj T[j ftXh j? fijVh fdZsh j'Jh fBors d/ T[sgkdB
d/ bJh ;kXBK d/ nkPktkdh ;z:'r iK fdZs/ j'J/ gbKN ns/ T[geoD Bkb T[sgkdB ehsh iKdh
j?. t;s{ d/ nkPktkdh ;z:'r dk fBoDk eodh j?. fJZe t;s{ d/ T[sgkdB ftZu seBheh tZyo/gD
dk fBoDk eoB d/ bJh th fJ;dk gq:'r j[zdk j?.

27H2 PosK ns/ ;XkoBheoD (Conditions and Generalisation)

o/yh gq'rokfwzr seBhe dk gq:'r e[ZM PosK ns/ ;XkoBheoD T[Zs/ fBoGo eodk j?.
gfjbk, fJZe fBPfus T[d/P j[zdk j?. fJj T[d/P bkG iK nkwdB B{z tZX s'A tZX pBkT[Dk iK
bkrsK B{z fBT{Bsw eoBk j' ;edk j?. fJ;B{z T[d/P cbB (objective function) iK e;"Nh cbB
(tenterion function) efjzd/ jB. i/eo fJZe wksok tZX s'A tZX pDdh j? sK T[;dh foDkswe
wksok fBT{Bsw pD iKdh j?. jo/e nfXeheoD ;wZf;nk dk d'jo/ (dual) fBT{BswheoD dh
;wZf;nk j[zdh j?. w[Zb ;wZf;nk gqw[Zy (primal) ;wZf;nk j?, fi;dh jw/Pk fJZe d'joh j[zdh j?.
i/eo gqw[Zy ;wZf;nk dk ;zpzX nfXeheoD Bkb j't/, sK d'joh dk fBT{BswheoD Bkb j't/rk ns/
ftgohs th.
d{i/, T[d/P B{z g{ok eoB d/ bJh t?ebfge T[sgkdB fefonktK (processes) j'Dh ukjhdh j?.
fefonk iK fefonkPhbsk (activity) dk ftuko o/yh gq'rokfwzr ftZu pj[s fInkdk wjZstg{oD
j?. gqfefonk “fe;h nkofEe ezw B{z eoB dh ftP/P ftXh j?.” fJj “fe;h soQK dh G"fseh
fefonk j[zdh j?, fit/A fe;h t;s{ dk T[gG'r eoBk, fe;h dk ;zrqfj eoBk, fe;h dk eo eoBk,
fe;h t;s{ B{z ;[ZN d/Dk ns/ fJZe ftP/P Yzr Bkb fe;h t;s{ dk T[sgkdB eoBk.@

B'N; o/yh gq'rokfwzr seBhe fBoDk eoB tkbh J/iz;h dh fJ; rZb ftZu ;jkfJsk eodh
j? fe T[j T[d/P B{z g{ok eoB d/ bJh ;G s'A fInkdk ;woZE ns/ fwsoe gqfefonk
u[D ;eD.

fsZi/, ;wZf;nk d/ e[ZM gqfspzX (constraints) iK nto'Xe (restraints) th io{o j[zd/ jB. T[j
;wZf;nk dhnK ;fEshnK Bkb ;zpzXs ;hwktK iK o[ektNK j[zdhnK jB fijVhnK fJj dZ;dhnK
jB fe eh^eh ehsk ik ;edk j? ns/ eh^eh eoBk io{oh j?. fJBQK B{z n;wkBsktK
(inequalities) th efjzd/ jB. T[sgkdB ftZu brGr T[j G{wh, fwjBs ns/ g{zih dhnK fdZshnK
j'JhnK wksoktK j[zdhnK jB, fiBQK dk fBPfus T[d/P B{z g{ok eoB d/ bJh ;woZEk gqfefonk
ftZu gq:'r j[zdk j?.

u"E/, ‘u'D uo’ (choice variables) th j[zd/ jB. fJj T[j ;z;EktK jB fiBQK dh u'D ehsh iKdh
j?, sK fe T[d/P cbB B{z tZX s'A tZX iK fBT{Bsw pDkfJnk ik ;e/ ns/ ;G o[ektNK B{z ;zs[PN
ehsk ik ;e/.
nkyoh, ;zGkte (feasible) ns/ nkPktkdh (optimal) jZb j[zd/ jB. T[gG'esk dh nkwdB ns/
t;s{nK dhnK ehwsK fdZshnK j'JhnK j'D s/, t;s{nK d/ ;G ;zGt ;z:'r, fiBQK B{z fJj ;zGkte
o{g s'A yohd ;edk j?, ;zGkte jZb j[zd/ jB. T[gG'esk d/ bJh, d' t;s{nK d/ ;zGkte jZB T[j
;G ;z:'r j[zd/ jB, fijV/ piN o/yk s/ iK T[; s'A yZp/ gk;/ ;fEs j'D id'A fe ;wbkrs o/yk
(isocost line) s/ T[j iK sK T[; s/ iK T[;d/ ;Zi/ gk;/ B{z ;fEs j[zd/ jB.

344 LOVELY PROFESSIONAL UNIVERSITY