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CODE No.:10BT60301
SREE VIDYANIKETHAN ENGINEERING COLLEGE(An Autonomous
Institution, Affiliated to JNTUA, Anantapur)
III B.Tech II Semester (SVEC10) Supplementary Examinations
December !01"
OPERATIONS RESEARCH[ Mechanical Engineeing !
Ti"e: 3 ho#$ Ma%. Ma&$: '0An$(e an) *I+E ,#e$-ion$
All ,#e$-ion$ ca) e,#al "a&$
1. a) Discuss the applications o# $perations %esearch to
en&ineerin& an' mana&erial problems.
b) n animal #ee' company must pro'uce !00 & o# a
mixture consistin& o# in&re'ients *1 an' *
'aily. *1 cost %s. + per & an' * %s. , per &.
-ot more than ,0 & o# *1 can be use' an' at
least /0 & o# * must be use'. in' ho much o# each
in&re'ient shoul' be use' i# the company
ants minimi2e cost.
. a) 3hat is 4un&arian metho' #or sol5in& an
assi&nment problem6 b) Consi'er the #olloin&
transportation cost table. The costs are &i5en in rupees7 the
supply an'
'eman' are in units. Determine an optimal solution.
Destination
Source 31 3! 3+ 3" 38 Supply
1 "0 +/ !/ +, +0 +!0
! +, !, +" +" 19, 8/0
+ +/ +, !" !, +0 ",0
Deman' +!0 +!0 "00 !"0 ",0
3. a) De#ine E.$.:. ;ist 5arious costs associate' ith
E.$.:. b) Determine the optimal replacement policy #or the
'ata &i5en belo<
=roup replacement cost %s. !0 per unit.
Cost o# in'i5i'ual replacement o# #ailure is %s. 90 per
unit.
Total number o# units in a system is 1000 units.
>ortality 'ata o# units to be use' in the system is as
#ollos<
Inter5al o# time perio' (hours) ?robability o# #ailure
0 !00 0
!00.01 "00 0.0/
"00.01 /00 0.+0
/00.01 ,00 0.",,00.01 1000 0.1/
/. a) Explain brie#ly @ho the replacement problems are
classi#ie'A.
b) leet o# cars ha5e increase' their costs as they
continue in ser5ice 'ue to increase' 'irect
operatin& cost (&as an' oil) an' increase' maintenance
(repairs tyres batteries etc..).The initial
cost is %s.+80000 an' the tra'e in 5alue 'rop as time passes
until it reaches a constant 5alue o#
%s."0000.=i5en the cost o# operatin& maintainin& an' the
tra'e in 5alue 'etermine the proper
len&th o# ser5ice be#ore cars shoul' be replace'.
ears o# ser5ice 1 ! + " 8
ear en' tra'e in 5alue (%s.) !90000 !10000 180000 110000
"0000
nnual operatin& cost (%s.) 11800 1!,00 1+/00 1"000 18000
nnual maintainin& cost (%s.) +000 8000 ,000 1!000 18000
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. a) De#ine the terms< Total ree an' In'epen'ent #loats.
b) Tass B C 4 I constitute a proect. The prece'ence
relationships are D7 E7
B 7 D 7 C =7 C 4 7 I 7 = I.
Dra a netor 'ia&ram to represent the proect an' #in'
the minimum time o# completion o# the
proect hen time in 'ays o# each tas is as #ollos<
Ta$& B C D E = 4 ITi"e , 10 , 10 1/ 1F 1, 1" 9
lso i'enti#y the critical path.
6. a) Deri5e the expression #or E$: an' state the assumptions
ma'e.
b) The annual 'eman' #or a pro'uct is /"000 units. The
buyin& cost per or'er is %s.10 an' the
estimate' cost o# carryin& one unit in stoc #or a year is
!0G. The normal price o# the pro'uct is
%s.10 per unit. 4oe5er the supplier o##ers a Huantity 'iscount
o# !G on an or'er o# at least
1000 units at a time an' a 'iscount o# 8G i# the or'er is #or at
least 8000 units. Su&&est the
most economic purchase Huantity per or'er.
'. a) In'icate the 'i##erence beteen 'ecision main& un'er
ris an' uncertainity in
Statistical Decision Theory.
b) manu#acturin& company has to select one o# the to
pro'ucts an' B #or manu#acturin&.
pro'uct reHuires an in5estment o# %s. !0000 an' pro'uct B
%s. "0000. >aret research
sur5ey hich shos hi&h me'ium an' lo 'eman's ith
correspon'in& probabilities an' sales
earnin&s in thousan's o# rupees #or the to pro'ucts is
&i5en in table. Construct an appropriate
'ecision tree. 3hat 'ecision shoul' the company tae6
Ma&e-Poaili-) Sale$
A B A B
High 0." 0.+ 80 ,0Me2i#" 0.+ 0.8 +0 /0
o( 0.+ 0.! 10 8
4. a) De#ine< i) ?ure Strate&y ii) >ixe' Strate&y
an' iii) Sa''le ?oint.
b) $btain the optimal strate&ies #or both persons an'
the 5alue o# the &ame hose payo## matrix is
as #ollos<
Pla)e APla)e B
B1 B B3 B/ B B6A1 " ! 0 ! 1 1
A " + 1 + ! !A3 " + F 8 1 !
A/ " + " 1 ! !
A " + + ! ! !
!
