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VED1
E L-LOVELY-H math29-1 IInd 21-10-11 IIIrd 24-1-12 IVth 21-4-12 Vth 20-8-12 VIth 10-9-12

fJekJh^29 L o/ykfuZso ftXh

dot gqsh feb'rqkw 1000 e?b'oh ns/ gq'NhB dh 50 rqkw wksok j?l ns/ wZyD d/ 2000 e?b'oh ns/ B'N
200 rqkw gq'NhB gqsh nZXk feb'rqkw j?. nkdoP nkjko ftZu gqshfdB 3000 e?b'oh ns/ 200 rqkw
gq'NhB ukjhdk j?. 500 rqkw p?qZv dh wkofeN ehws o[H 2 ns/ wZyD dh gqsh 500 rqkw ehws o[H 6
j?.
;wZf;nk fJj j? fe T[Zgo ;{uh d/ nkyoh ekbw ftZu fdZs/ rJ/ fBT{Bsw g'Pe^nkjko^nkdoP d/
nB[;ko ;G s'A T[Zu nkjko ns/ gqPBfuzBQ (<) d[nkok gqrN ehsh rJh fBT{Bsw bkrs eh j'Dr/.
nkjko dh e[ZbQ bkrs
Minimise

Subject .....(1)

ns/
fBT{Bsw ehsh ikD tkbh bkrs C j?, fijVh d'B'A x 1 ns/ x 2 uoK dk o/yh cbB (linear function)
j?. gkoPt ;zpzX 3 ns/ 8 n;wkBsktK jB fijVhnK fdZs/ j'J/ nkjko d/ gqkgs ehs/ ikD tkb/
fBT{Bsw g'Pe nkjko nkdoP B{z gqrN eodh jB. ;wZf;nk o/yh j? feT[Afe o/yh n;wkBsktK d/
ofjzd/ j'J/ nfoDkswe uo (non-negative veriables) fBT{Bsw pDkT[D/ jB. fszB'A ftZu'A fe;/ d'
f;EshnK Bkb jZb j' ;edk j?. T[dkjoD d/ bJh, fJZe gkoPt ;zpzX (side relation) d/ j[zd/ j'J/
bkrs C B{z fBT{Bsw pDkfJnk ik ;edk j?L x 1 + 2x 2 = 3 fJ;B{z jZb eoB s/L x 1 = 3 ns/ x 2 = 3/2
= 1.5 fuZso 29H2 ftZu fJ;B{z AB o/yk d[nkok ftnes ehsk frnk fiZE/ OA = 1.5x 2 ns/ OB =
3x 1 .
d{ik gkoPt ;zpzXh j?L 2x 1 + 8x 2 = 8
ns/ fJ;B{z jZb eoB s/, x 1 = 4 ns/ x 2
= 1 gqkgs j[zd/ jB. fJ;B{z fuZso 29H2
ftZu CD o/yk d[nkok fyZfunk frnk j?
fijVk fJ; ;wheoD B{z ;zs[PN eodk j?
fiZE/ OC = 1x 2 ns/ OD = 4x 1 .
fJ; soQK fuZso ftZu x 1 (pq?Zv) ;wKso
neP T[Zs/ ns/ x 2 (wZyD) nB[bzp neP
T[Zs/ wkg/ rJ/ jB. AB o/yk ;wheoD
x 1 + 2x 2 = 3 ns/ CD o/yk ;wheoD
2x 1 + 8x 2 = 8 B{z ftnes eodhnK jB.
;zGkte jZb w'Nh o/yk AZD T[Zs/ iK T[;d/ T[Zgo j't/rk. fJj ;kvh ;wZf;nk ftZu Z fpzd{ T[Zs/ j[zdk
j? fiZE/ d'B'A o/yktK AB ns/ CD eZNdhnK jB.
fJj gsk eoB d/ bJh fe ;zGkte jZb Z T[Zs/ jh j[zdk j? iK A iK D fpzd{ T[Zs/, n;hA ;wZf;nk d/
d'B'A ;wheoDK B{z :[rws ;wheoDK d/ o{g ftZu jZb eod/ jBL
x 1 + 2x 2 = 3 .....(1)
2x 1 + 8x 2 = 8 .....(2)
T[dkjoD L wzfBnk fJZe T[sgkdB fdZs/ j'J/ gqfspzXK (Constraints) d/ nzsors nkgDk nkrw
(Revenue) tZX s'A tZX eoBk ukj[zdk j?. wzfBnk fJZe cow d' T[sgkd X 1 ns/ X 2 dk T[sgkdB
eoBk ukj[zdh j? ns/ T[;d/ bJh T[;d/ e'b j/m nB[;ko fszB ;kXB a, b ns/ c fdZs/ j'J/ jB^

a = 40, b = 50, c = 42

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