64 m kj izns'k jktf"kZ V.Mu eqDr fo'ofo|ky;] bykgkckn

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34 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
Job 1 2 3 4 5 I 12 8 7 12 14 II 8 6 17 16 8 III 7 6 12 4 9 IV 9 9 14 8 12 7 6 12 10 8 6 Solve the game whose pay off matrix is given below: 3 bl xse dks gy djsa ftldk is vkQ esfVªDl fuEu gSA PLAYER B B 1 B 2 B 3 A 1 2 2 2 A 2 0 4 0 A 3 1 -3 -1 7 Define the following : 3 ifjHkkf"kr djsaA (a) Basic feasible solution (b) Degeneracy (c) Dual problem. 35
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Page 3 and 4: 3 5. Derive the wave equation for a
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Page 19 and 20: 19 - ;fn y = (sin 1 x) gks rks fn[k
Page 21 and 22: 21 é1 2 3ù A = ê ú ê 0 5 0 3
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Page 41 and 42: (ii) ftEuksLieZl dh vkfFkZd mi;ksfx
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87 6. efJeÅeeLeea meneÙelee mesJe
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153 OTHER INFORMATION : Volume 2 :
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64 m kj izns'k jktf"kZ V.Mu eqDr fo'ofo|ky;] bykgkckn

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