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VED1
E L-LOVELY-H math29-1 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 jo/e o/yh gq'rokfwzr ;wZf;nk d/ fszB Gkr j[zd/ jB. T[Zgo fbyh ;wZf;nk d/ T[j fJ; soQK jB.
(i) T[d/P cbB (Objective Function)LT[d/P cbB fJj dZ;dk j? fe i/eo d' t;s{nK X ns/ Y
gqsh fJekJh o[H 12 ns/ o[H 15 nkrw bkT[AdhnK jB sK fJBQK t;s{nK dhnK fezBhnK wksoktK
T[sgkds ehsh ikD fe cow tZX s'A tZX nkrw iK nkwdB nofis eo ;e/. fJ;B{z fJ; soQK
fbfynk ik ;edk j?^
Maximise R = 12 X + 15 Y
(ii) gqfspzX (The Constraints)LT[Zs/ dh ;{uh B{z j[D ;wheoDK d/ o{g ftZu gfotofss ehsk ik
;edk j? fijV/ gqfspzXK B{z ftnes eod/ jB fiBQK d/ nzsors cow ekoi eodh j?. fJj
;zouBkswe gqfspzX (structural constraints) ejkT[Ad/ jB.
gfjbK n;hA nkrw A B{z b?Ad/ jK. nkrs A dh tZX s'A tZX T[gbpX wksok 48 fJekJh j?.
gozs{ d'jK t;s{nK X ns/ Y dhnK wksoktK 48 fJekJhnK s'A tZX BjhA j' ;edhnK jB.
rfDse o{g ftZu, feT[Afe 12X + 4Y fJekJh 48 s'A tZX BjhA j' ;edh, fJ; bJh nkrs A dk
gqfspzX j't/rk L 12X + 4Y ≤ 48. fJ;h soQK d/ soe d[nkok B ns/ C nkrsK d/ gqfspzXK dhnK
n;wkBsktK B{z fbfynk ik ;edk j?. fJ; soQK ;kvh ;wZf;nk d/ fszB ;zouBkswe gqfspzX
jB^

12X + 4Y ≤ 48 .....(1)
6X + 12Y ≤ 72 .....(2)
14X + 12Y ≤ 84 .....(3)
(iii) nfoDkswe gqfspzX (Non-negative Constraints)L o/yh gq'rokfwzr ;wZf;nk ftZu
nfoDkswe gqfspzX th j[zd/ jB fijV/ fJ; wkBsk T[Zs/ fBoGo jB fe ;wZf;nk d/ jZb ftZu e'Jh
uoK d/ foDkswe w[Zb BjhA j' ;ed/ jB. fJ;dk Gkt j? fe X ns/ Y t;s{nK dk T[sgkdB Iho'
iK XBkswe j' ;edk j? gozs{ fJj foDkswe BjhA j' ;edk. fJ; soQK ;kvh ;wZf;nk d/
nfoDkswe gqfspzX jB X ≥ 0 ns/ Y ≥ 0H

29H1 ;wZf;nk dk o/ykfuZso jZb (The Graphic Solution of the

Problem)
o/ykfuZso jZb d/ bJh n;hA T[Zgo toDs ;wZf;nk B{z d[pkok fbyd/ jKL
Maximise R = 12X + 15Y
Subject to (i) 12X + 4Y ≤ 48 .....(1)

6X + 12Y ≤ 72 .....(2)
14X + 12Y ≤ 84 .....(3)
(ii) X ≥ 0, Y ≥ 0
jo/e n;wkBsk B{z o/ykfuZso d[nkok ftnes eoB d/ bJh, n;hA fszB'A ;wheoDK d/ n;wkBsk
fuzBQ (≤) B{z Szve/ pokpo (&) d/ fuzBQ b?Ad/ jK. fJ; soQK ;wheoD (1) B{z fJ; soQK fbud/ jKL
12X + 4Y = 48.
fJj wzB e/ fe t;s{ X e/tb nkrs A dhnK ;kohnK 48 fJekJhnK d[nkok T[sgkds ehsh
iKdh j? ns/ t;s{ Y fpbe[b BjhA j[zdkL
12X + 0 = 48 (at the maximum)
iK X = 4 (id'A Y = 0)

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