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VED1
E L-LOVELY-H math11-1 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 T[dkjoD 1L wzr ns/ g{osh cbB j/m nB[;ko j?^

5 1
q − p = ns/ q = 2p – 3
2 2
;zs[bB ehws ns/ wksok dZ;'.

jZb L ;zs[bB dh ;fEsh ftZu t;s{ dh wzr ns/ g{osh d'B'A ;wkB j'DrhnK, Gkt

iK

iK

d[pkok

p dk wkB oZyD s/

2
2
T[dkjoD 2H i/eo d' t;s{nK d/ bJh T[g:'rsk cbB U = 3x y j? ns/ piN ;hwk 2x +
3y = 18 j't/ sK X s/ Y t;s{nK dh wzrhnK ikD tkbhnK wksoktK B{z gsk eo'.
jZb (Solution)L fdZsh j'Jh T[g:'rsk cbB j?^
2 2
U = 3x y
ns/ piN ;hwk (budget constraint) j?^

2x + 3y = 18
iK 2x + 3y – 18 = 0
b/Aro/Ai r[De dk gq:'r eoB s/ wzr cbB j't/rh^
2 2
V = 3x y + λ (2x + 3y – 18) ....(i)
wzr cbB dk ‘x’‘y’ ns/ ‘λ’ d/ ;zdoG ftZu tZy^tZy fBy/VB nzfPe ehsk ikt/rk. fco T[; s'A
pknd T[g:'rsk B{z nfXeheoD eoB d/ bJh gfjb/ fBy/Ve (first derivative) B{z Iho' d/ pokpo
oZyD s/^
....(ii)

....(iii)

....(iv)

;wheoD (2) ns/ (3) B{z b?D s/

−λ 6 xy 2 2 y
2
= iK = iK 2 3x = y
−λ 6xy 3 x
2
3
iK x = (3/2)y
x dk wkB ;wheoD (iv) ftZu oZyD s/
2 × (3/2)y + 3y – 18 = 0

176 LOVELY PROFESSIONAL UNIVERSITY