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93
m kj izns’k jktf"kZ V.Mu eqDr fo’ofo|ky;] bykgkckn
vf/kU;kl (Assignment) 2012-2013
Lukrd dyk dk;ZØe
Under Graduate Art Programme
fo’k; % xf.kr
Subject : Mathematics
dkslZ “kh’kZd % Linear Programming
Course Title : Linear Programming
fo’k; dksM% ;w0th0,e0,e0
Subject Code : UGMM
dkslZ dksM % ;w0th0,e0,e0-12
Course Code : UGMM-12
vf/kdre vad % 30
Maximum Marks:30
Section - A
[k.M & d
vf/kdre vad % 18
Max. Marks : 18
uksV % nhkZ mRrjh; iz”uA vius iz”uksa ds mRrj 800 ls 1000 “kCnksa esa fy[ksaA lHkh iz”u vfuok;Z gSA
Note : Long Answer Questions. Answer should be given in 800 to 1000 words.
Answer all questions.
1(a) Show that Dual of the dual of a primal L.P.P. is the primal L.P.P itself.
fn[kkb;s fd izkbey ds }Sr dk }Sr Hkh ,d izkbey gksxkA 3
(b) Show that the set of all feasible solutions of on L.P.P. is a convex set.
fn[kkb;s fd L.P.P. ds fQftcy gky dk leqPp; ,d convex leqPp; gksxkA 3
2(a) Obtain the dual of the following L.P.P. minimize Z = 2x2 + 5x3
subject to L.P.P. dk }Sr Kkr djsaA 3
x + x ³ 2
(b)
1
2x
x
1
2
+ x
- x
2
+ 6x
+ 3x
1 2 3
1
, x2
, x3
³
3
£ 6
= 4
and x 0
Use simplex method to solve the following L.P.P. maximize
Z = 4x1 + 10x2
subject to constanits
flEiysDl fof/k ls L.P.P. iz'u dks gy djsaA 3
3(a)
(b)
2x
1
2x
1
2x
+ x
2
+ 5x
+ 3x
1
1
, x2
³
£ 50
2
2
£ 100
= 90
and x 0
Solve the following linear programming problem graphically:
L.P.P. iz'u dks fp= fof/k ls gy djsaA 3
Z = x 1
+ x subject to constanits
Maximize
2
x + x £ 1
1
- 3x
2
+ x
1 2
1
³ 0,
x 2
³
³ 3
and x 0
Define saddle point for the person two choice zero sum game. Is it necessary
that two person two choice zero sum game always posses a saddle point.
lSMy fcUnw dks ifjHkkf"kr djsa nks O;fDr;ksa ds 'kwU; ;ksx [ksy ds fy, D;k nks O;fDr;ksa ds 'kwU;
[ksy esa lSMy fcUnq vo'; :i ls gksrk gSA 3
Section - B
[k.M & [k
vf/kdre vad % 12
Max. Marks: 12
uksV % ykq mRrjh; iz”uA vius iz”uksa ds mRrj 200 ls 300 “kCnksa esa fy[ksaA lHkh iz”u vfuok;Z gSA
Note : Short Answer Questions. Answer should be given in 200 to 300 words.
Answer
all questions.
4 Solve the following transportation problem: 3
VªkUliksVs'ku iz'u dks gy djsaA
W 1 W 2 W 3 Supply
F1 3 6 5 5
F2 3 4 1 7
F3 6 6 8 8
F4 2 8 4 20
Demand 8 10 22 40
5 Solve the following assignment problem: 3
,lkUesUV iz'u dks gy djsaA
Man