Page 361 - DECO403_MATHEMATICS_FOR_ECONOMISTS_PUNJABI

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

fJ;h soQK fJj wzB e/ fe ;kohnK 48 fJekJhnK B'N
s'A e/tb Y t;s{ jh T[sgkds ehsh iKdh j? sKL
0 + 4Y = 48
iK Y = 12 (id'A X = 0)
;wheoD 12X + 4 Y = 48 B{z fuZso 29H1 ftZu AB
o/yk d[nkok ftnes ehsk frnk j? fiZE/ OA = Y
ns/ OB = 4X. o/yk AB T[Zs/ e'Jh th fpzd{ fit/A T
;wheoD 12X + 4Y = 48 B{z ;zs[PN eodk j?
feT[Afe fJ; o/yk AB d/ fBZu/ ns/ yZp/ gk;/ dk
y/so n;wkBsk 12X + 4Y ≤ 48 B{z ;zs[PN eodk
j?.
fJ;h soQK ;wheoD 6X + 12Y = 72 B{z jZb eoB
s/ X = 12 ns/ Y = 6 gqkgs j[zd/ jB fiBQK B{z fuZso 29H1 ftZu CD o/yk d[nkok do;kfJnk frnk
j? fiZE/ OC = 6Y ns/ OD = 12X ns/ ;wheoD 14X + 12Y = 84 B{z jZb eoB s/ ;kB{z gqkgs j[zdk
j?, X = 6 ns/ Y = 7 fiBQK B{z fuZso 29H1 ftZu EF o/yk d[nkok fdykfJnk frnk j? fiZE/ OE = 7Y
ns/ OF = 6X.
;zGkte y/so (Feasible Region)^fuZso 29H1 fJj fdykT[Adk j? fe goSkt/A tkb/ (shaded) y/so
ftZu fpzd{ fijV/ fJZe^d{i/ B{z eZNdhnK j'JhnK fszB'A o/yktK d[nkok d[nkok fxo/ j'J/ jB jo/e fszB'A
n;wkBsktK B{z ;zs[PN eoDr/. fpzd{ S T[Zs/ EF o/yk CD o/yk B{z eZNdh j? ns/ fpzd{ T T[Zs/ CD
o/yk AB B{z eZNdh j?. fJ; soQK OBTSC y/so fijV/ fszB'A o/yktK d/ fJZe^d{i/ B{z eZND tkb/ S ns/
T fpzd{nK d/ yZp/ gk;/ fBZu/ ;fEs j?, fszB'A ;wheoDK dhnK n;wkBsktK B{z ;zs[PN eodk j?. fJj
goSkt/A tkbk (shaded) y/so T[sgkdB dk ;zGkte y/so ejkT[Adk j? ns/ jo/e fpzd{ fijVk fJ;
y/so d/ nzdo iK fJ;dh ;hwi T[Zs/ j[zdk j? ;wZf;nk dk ;zGkte jZb ftnes eodk j?.
nkPktkdh jZb (Optimum Solution)^ftfGzB fpzd{ B, T, S, C fijV/ ;zGkte jZb B{z ftnes eod/
jB, fJBQK ftZu'A fejVk nkPktkdh fpzd{ j? fijVk cow d/ nkrw B{z tZX s'A tZX eo/rk< fJ; fpzd{ B{z
phi rfDs d[nkok fet/A ikfDnk ik ;edk j?<
n;hA ;wheoDK (1) ns/ (2) d[nkok fpzd{ B ns/ C d/ fBod/P^nzeK (coordinates) B{z ikDd/ jK
fiBQK d/ nB[;ko OB = 4X ns/ OC = 6Y. fpzd{ T d/ fBod/P^nzeK B{z fBoXkfos eoB d/ bJh
n;hA ;wheoDK (1) ns/ (2) B{z :[rws ;wheoDK d/ o{g ftZu b?Ad/ jK. (feT[Afe o/yktK AB ns/
EF fpzd{ T T[Zs/ eZNdhnK jB) ns/ fJBQK B{z jZb eod/ jBL
12X + 4Y = 48 .....(1)
14X + 12Y = 84 .....(3)
;wheoD (1) B{z 3 Bkb r[Dk eoe/ ns/ ;wheoD (3) B{z T[; ftZu'A xNke/L
36X + 12Y = 144
14X + 12Y = 84
22X = 60
X = 2.73
;wheoD (1) ftZu X = 2.73 d/ w[Zb B{z brke/,
12X 2.73 + 4Y = 48
32.76 + 4Y = 48
4Y = 48 – 32.76
iK 4Y = 15.24
Y = 3.81

LOVELY PROFESSIONAL UNIVERSITY 355