Page 364 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

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 n;hA fJj th wzB fbnk X 1 dh fJZe fJekJh dk T[sgkdB eoB d/ bJh T[;B{z j/m nB[;ko jo/e
;kXB dh io{os j't/rh^
a = 4, b = 10, c = 6
[
fJ;h soQK n;hA fJj th wzB fbU fe X 2 dh fJekJh dk TsgkdB eoB d/ bJh T[;B{z j/m
nB[;ko jo/e ;kXB dh io{os j't/rh^
a = 10, b = 5, c = 7
n;hA fJj th wzB fbnk fe X 1 ns/ X 2 dh gqsh fJekJh ehws eqw nB[;k 5 o[gJ/ ns/ 7 o[gJ/
j?. fJ; soQK T[j T[sgkde fdZs/ j'J/ ;kXBK T[Zs/ nkgDh e[ZbQ nkwdB (Total Revenue) tZX s'A
tZX eoBk ukj/rk. rfDse o{g ftZu, T[d/P cbB^
Max TR = 5X 1 + 7X 2 = Z

cow s/ gqfspzX fdZs/ j'J/ jB ns/ cow T[jBK ;kXBK s'A tZX T[g:'r BjhA eo/rh^
4X 1 + 10X 2 ≤ 40 ....(i)
10X 1 + 5X 1 ≤ 50 .....(ii)
6X 1 + 7X 2 ≤ 42 .....(iii)
fJZE/, X 1 , X 2 ≤ 0
cow d/ fJBQK gqfspzXK B{z j/m nB[;ko do;kfJnk ik ;edk j?^

gfjbk gqfspzX fJj dZ;dk j? fe a ;kXB fijVk fe X 1 ns/ X 2 d/ T[sgkdB d/ gq:'r ftZu
fbnkfJnk iKdk j?. T[j ;kXB ‘a’ dh e[ZbQ g{osh s'A tZX BjhA j' ;edk. fJj ;kXB g{osh s'A
xZN iK pokpo j' ;edk j?, tZX BjhA. fJ;h soQK d/ j'o gqfspzXK d/ ;zpzX ftZu j't/rk. fJZE/
n;hA o/yh gq:'iB B{z rqkc dh ;jkfJsk Bkb do;ktKr/.
;G s'A gfjbK n;hA X 1 ns/ X 2 d/ fBod/Pe nze eZYKr/, fi;d/ bJh n;hA fBopZX ;wheoDK
dhnK n;wkBsktK (Inequalities) jNk fdnKr/ ns/ fJ; soQK n;hA fszB seBhehnK d/ fBod/Pe
nze (10, 4), (5, 10) ns/ (7, 6) gqkgs j'Dr/. fJjh seBhehnK gq:'iB ;wZf;nk dk ;zGkts
jZb (Feasible Solution) gqrN eoBrhnK. fuZso ftZu X-neP T[Zs/ X 1 T[sgkd ns/ Y-neP
T[Zs/ X 2 T[sgkd wkfgnk frnk j?. fJZE/ cow d[nkok ngDkJ/ rJ/ fszB gqfspzXK d/ fBod/Pe
nzeK dh ;jkfJsk d[nkok rqkc d[nkok fJZe ;ob o/yk d/ o{g ftZu do;kJ/ rJ/ jB. Z 1 ^T[d/P
cbB (Objective Function) j?.

wzfBnk T[sgkde a ns/ b gqfspzXK B{z
gq:'r ftZu fbnkT[Adk j? sK cow d/
bJh OAMG y/so ;zGkts y/so
(Feasible Zone) gqkgs j't/rk. fJ;h
soQK i/eo T[j a ns/ c gqfspzXK dk
gq:'r eodk j? sK T[;B{z y/so OATK
;zGkts y/so gqkgs j't/rk. fJ;h soQK
i/eo cow b ns/ c gqfspzXK B{z gq:'r
ftZu fbnkT[Adh j? sK y/so OLNG
;zGkts y/so gqkgs j't/rk. i/eo T[j
fszB'A gqfspzXK a, b ns/ c B{z fJeZm/ ezw
ftZu fbnkT[Adk j? sK T[;B{z y/so
OAMG d/ pokpo ;zGkts y/so gqkgs
j't/rk. cow dk ;zgkts jZb fJ;
y/so d/ nzsors jh j't/rk.

358 LOVELY PROFESSIONAL UNIVERSITY