11. Major Core 10.Optimization Techniques
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HOLY CROSS COLLEGE (Autonomous) , TIRUCHIRAPPALLI -620 002. DEPARTMENT OF MATHEMATICS III B.Sc. MATHEMATICS( SHIFT I & II) , SEMESTER –V , I INTERNAL TEST : AUGUST 2015 MAJOR CORE 10: OPTIMIZATION TECHNIQUES I Time : 2 Hours Code: U08MA5MCT12 Max. Marks : 50 SECTION – A 10 x 1 = 10 ANSWER ALL THE QUESTIONS: Choose the Correct answer: 1. In the set of all feasible solutions to a L.P.P. by graphical method ,an optimal solution using the feasible region is at a) all points b) at any point c)only at an extreme point d) an interior point 2. In the standard form of L.P.P.,the constraints should be a) ≤ type b) ≥ type c) inequalities d) equations 3. The condition for selecting a variable into basis in simplex method is a) b) c) d) 4. Match the following methods of finding an initial basic feasible solution to a transportation problem, with an appropriate position of a cell for initial allocation and choose the correct answer. 1. North West Corner rule A. min ( i , 1 ) for i = 1,2,… 2. Row Minima method B. (1 ,1 ) 3. Column Minima method C. min ( i , j) for i, j = 1,2,… 4. Matrix Minima method D. any (i , j ) E. min ( 1 , j ) for j= 1,2,… a) 1C,2E,3A,4B b) 1B,2E,3A,4C c) 1A,2E,3D,4B d) 1B,2E,3A,4D
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Transcript of 11. Major Core 10.Optimization Techniques
HOLY CROSS COLLEGE (Autonomous) , TIRUCHIRAPPALLI -620 002.DEPARTMET O! MATHEMATICSIII ".S#. MATHEMATICS( SHI!T I $ II) , SEMESTER %& , I ITERAL TEST 'AUGUST 20()MA*OR CORE (0' OPTIMI+ATIO TECHI,UES IT-m. ' 2 Hou/s Co0.' U01MA)MCT(2M23. M2/4s ' )0SECTIO % A (0 3 ( 5 (0AS6ER ALL THE ,UESTIOS'C7oos. t7. Co//.#t2ns8./'(.In t7. s.t o9 2:: 9.2s-;:. so:ut-ons to2 L.P.P. ;< =/2>7-#2: m.t7o0 ,2n o>t-m2: so:ut-onus-n= t7. 9.2s-;:. /.=-on -s 2t 2) 2:: >o-nts ;) 2t 2n< >o-nt#)on:< 2t 2n .3t/.m. >o-nt 0) 2n -nt./-o/ >o-nt2. In t7. st2n02/0 9o/m o9 L.P.P.,t7. #onst/2-nts s7ou:0 ;.2)?t. ;)@t. #)-n.Au2:-t-.s 0).Au2t-onsB. T7. #on0-t-on 9o/ s.:.#t-n= 2 C2/-2;:. -nto ;2s-s -n s-m>:.3 m.t7o0 -s2) ( )0 < m-n D - #E E ;) ( )m23 D - # F 0E E #) ( )m23 D - # G 0E E 0) ( )m-n D - # F 0E EH. M2t#7 t7. 9o::o8-n= m.t7o0s o9 9-n0-n= 2n -n-t-2: ;2s-# 9.2s-;:. so:ut-on to 2t/2ns>o/t2t-on >/o;:.m, 8-t7 2n 2>>/o>/-2t. >os-t-on o9 2 #.:: 9o/ -n-t-2: 2::o#2t-on 2n0 #7oos. t7. #o//.#t 2ns8./.(. o/t7 6.st Co/n./ /u:. A.m-n ( - , ( ) 9o/ - 5 (,2,I 2. Ro8 M-n-m2 m.t7o0".(( ,( ) B. Co:umn M-n-m2 m.t7o0 C. m-n ( - , E) 9o/-, E 5 (,2,I H. M2t/-3 M-n-m2 m.t7o0 D.2n< (- , E ) E.m-n ( ( , E ) 9o/ E5 (,2,I 2) (C,2E,BA,H" ;) (",2E,BA,HC #)(A,2E,BD,H" 0)(",2E,BA,HD). O9 t7. 9o::o8-n= >2-/ o9 st2t.m.nts, on. -s 2n 2ss./t-on 2n0 t7. ot7./ -s t7. >oss-;:. /.2son. R.20 t7. st2t.m.nts #2/.9u::< 2n0 m2/4 t-on2: -n t7. 0.#-s-on C2/-2;:.s -nCo:C.0 -n 2 L.P.P..2) "ot7 t7. 2ss./t-on 2n0 t7. /.2son 2/. t/u. st2t.m.nts 2n0 t7. /.2son -s 2n 20.Au2t. .3>:2n2t-on 9o/ t7. 2ss./t-on.;) "ot7 t7. 2ss./t-on 2n0 t7. /.2son 2/. t/u. st2t.m.nts 2n0 t7. /.2son 0o.s not .3>:2-ns t7. 2ss./t-on.#) Ass./t-on -s t/u. st2t.m.nt ;ut t7. /.2son -s 92:s. st2t.m.nt.0) "ot7 t7. 2ss./t-on 2n0 /.2son 2/. 92:s. st2t.m.nts.Ans8./ t7. 9o::o8-n= -n 2 s.nt.n#. o/ t8o ' 6. D.9-n. 2 #onC.3 s.t.J. 67.n -s 2 so:ut-on to 2 L.P.P.;< =/2>7-#2: m.t7o0s2-0 to ;. un;oun0.0K1. D.9-n. 2 0.=.n./2t. ;2s-# 9.2s-;:. so:ut-on to 2 =.n./2: L.P.P.L.St2t. t7. #on0-t-on 9o/ o>t-m2:-to/t2t-on >/o;:.m ;< MODI m.t7o0.(0.672t -s t7. -n0-#2t-on 2n 2:t./n2t. o>t-m2: so:ut-on -n 2 t/2ns>o/t2t-on >/o;:.mKSECTIO % " B 3 ) 5 ()AS6ER ALL THE ,UESTIOS, SELECTIG OE !ROM EACH SET'(((2)So:C. =/2>7-#2::o/t2t-on >/o;:.m.3>:2-n-n= t7. st.>s.To AC2-:2;-:-t
