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Seventh Semester B.E. Degree Examination, June/July 2Ol4Operations Research

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"'n;"""'"' " at least TWo questions -from each pait. ::::, .''1""'-.,,. 2. [.Ise of statistical tables permitted. ,1,"r,,,,,, .

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1 a. fi"ist'"4nd explain the various phases of OR problems. , , ' (06 Marks)

b. WfrU'ilre ltre limitations of OR? . ,::,, ;'

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c. e mail[#bturer of a line of patent medicines is preparing a produgfio{nlan^gl medicines Aand B. T'h@re are sufficient ingredients available to make 20,000 qo'ttles of 'A' and 40,000

bottles of 'k}fiUt three are only 45,000 bottles into which e,iffi'of the medicines can be

put. Furthermb& it takes 3 hours to prepare enough material to filI 1,000 bottles of 'A', ittakes t hour to pepare enough material to fill 1,000 bottles of 'B' and there are 66 hoursavailable for this openesion. The profit is {8 per ba#.19 feir 'A' and t7 per bottle for 'B'.Formulate the problem'aq4LPP and solve by graphibdmethod. (10 Marks)

2 a. Define slack, surplus, and artifiiial variables,o- (06 Marks)

b. Obtain the dual of the following,ffimal LP pmblem:Minimize Z:xt * 12 * x3

Subjectto xr -3xz +4xt:5 q 5* Zxr-2a<3Zv,z-xz) J .'''';\r' X,*' Xt, X2 ) 0, xs unrestricted. (g4Marks)

c. Use Big-M method to solve the fotrbwing Lm*, ,Minimize Z:4x1 +2xz ,.:.

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Subjectto 3xr*xz)27",-1. ; -x1.-2a<-21

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for the above situation considering all the data given.(12 Marks)

x1 + 2x2 >'30 ; xi , x#k 0 (10 Marks)

3 a. A company has$dts A, B and C which have capacity q$,1,prgduce 300, 200 and 500 kgrespectively gq h iarticular chemical/day. The production dos pgl kg in these plants are

{0.70, < t0.66 respectively. Four bulk consumers have placed orders for the

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'!ar''r :: : Shipping costs in paise/kg from plants to consumers are given below: i:, ,.,,..

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From Plants BC

Workout the optimum schedule

Price offered T

35468 lt 9 12

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b. A company has a team of four salesman and there are four districts where the companywants to start its business. The company estimates that the profit/day is given below. Findthe assignment of salesman to districts which gives maximum profit.

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t4 11 15 15

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{!,4 a. Expldifutfre branch and bound method in integer programming. .. . ,, (06 Marks)

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b. Use Gomaffifiactional cutting plane method to solve the follffiipg IPP.

sil:Til mr*2,. -

5x1 + &$,9 15

x1 , xltO.,-.and are integers. . (14 Marks)

-r JeffBrrJ sffi,xr , xT*,9,:,,,ftnd are integers.

. ,,,_:,,, _a9;rffiu are integers'

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(05 Marks)5a.

b. A small projectActivity *Brceeedin8 activi$'' ;Time estimates (weeks)

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E A 7 7.5 , 11

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;$' Draw the PERT network for the project. " ,, ,. ..(..;tii) Determine the critical path and prepare the activity schedule for the project.

(iii) If a 30 week deadline is imposed, what is the probability that the project wilibecompleted within the time limit?

b. A postal clerk can service a customer in 3 minutes. The service time is being exponentiallydistributed. The inter arrival time of customers is also exponentially distributed with an

average of 12 minutes during early morning slack period and an average of 5 minutes duringthe afternoon peak period. Assess the average queue length and the expected waiting time in

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(06 Mark$)-r"'

the queue during the two periods.

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(14 Marks)

7 a. Explain the following:(i) Pay off matrix (ii) Saddle point (iii) Fair game.

b. Exnlain the rule of dominance.

n; 'r-l,pr, Use of property of dominance to solve the following game.B

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lapsed time for the(06 Marks)

8a.

b.

State the assumptions madewhile dealing with*$q+Wncing problems.

*"t"Find the sequence for the followfug Uf jobs tht will minimize the total

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Threadins (B) - '1 8 b=""., 4 6 J I13 l&#-,? P^

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Job 1Sequence: A B C D ,., ETime(hr): 6 8 4 12 4"'

Job2 Sequence: B C A D ETimeftr): 10 8 6 4 12

.Hc. Use graphical meth.dQ:tb minimize the time required to process the following jobs on themachines. CalcuXat+the total elapsed time to complete th-e,.jqbs: For each machine specify

"' . .""-: (10 Marks)the job that s-ho.rMb" dor. firsl

three operations:

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Seventh Semester B.E. Degree Examination, June/July 201,4

Robotics':i:::,,

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oo6 ^.^-E rr,",,f,*.,, PART - AE I a. Witf i:""eat sketch, name variour typ. of -Uot joints and also shp#'\heir symbols and

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I degredbffi,freedom. r ,,,1* (lOlvtarks)H r a. wrth**neat sketch, name varlous type oI robot Jomts ano also snpw'${rer symDors an

5 degrees of freedom (lo Mark:g b. Find the'resirltant rotation matrix with Euler's angle representatiorr$r rotation in sequence:fr b. Find the resirltant rotation matrix with Euler's angle representatiortfr rotation in sequence:

, * i) i)Rotation of Y about u axis (R,Y) - YawiixS= ii) Rotation of'0ra.hout v axis (R"0) - pitch ,,. ,,,.

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t 3 iii) Rotation of Q abpqt w axis (R*0) - Roll (10 Marks)

}[ Z a. Draw a neat oiug.u- jTSCARA manipulato, *a n,{l$k final transformation matrix of end

E $" eflectors using D-H parameffi,4nd write the equatbn of position and orientation. (14 Nlarks)

E A' b. Explain direct and inverse kineir,tatics probleqg;-." (06 Marks)e6I =

3 a. Explain velocity ellipse for a plan#:&anipulator. (10 Marks)

E .g b. fxpUin statics seriai manipulator ru,itfii=free body diagram of link. (10 Marks)

BE5 R 4 a. Derive the equation of motion ef d*iilaner 2R'rpaipulator using Lagrangian formulation.

E S (lo Marks)

.$: b. Derive the equation of ffiiOns of two degree fiqg$br, spring-mass damper systems using

; E Lagrangian formulatioru:\ (10 Marks)

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E * 5 a. What is trajeetory planning? Explain the two common approaches used to plan manipulator

+ H trajectory. (10 Marks)

8 i b. Write a short note on Cartesian straight line motion and Cartesian'bifcnlpr motion. (10 Marks)

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E € 6 ?. Ex41&ffi PID control of single link manipulator. '''u'

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X E b. Explain force control of a single mass system ', ;.'",, (10 Marks)?a^.=ntsg g 7 a. With a neat sketch, explain the basic principle of operation and working of a stepper rnotor.6 = (lo Marks)EEtE (I,#arks)

E A b. Write the comparison of characteristics of hydraulic, electric and pneumatic actuators._ -I a (I0 Marks)\Jq

With a neat sketch explain.the basic principle and working of resolver. (10 Marks)

Name different types of proximity sensors and with neat sketch explain any two types ofproximity sensors. (10 Marks)

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Seventh Semester B.E. Degree Examination, June/July 201,4

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Mechanica! Vibrations r" " "

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Note: Answer any FIWfull questions, selecting .<k:.atleast TWO questionsfrom each part.

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a. Explain frdCh6rgy method of finding natural frequency of a spriti!1*iugps system. (08 Marks)

b. f,rn0. 1ffijatural frequency of the spring controlled simple penduli wn in Fig.Q.2(b).Neg@themassoftherod. _ , , r / r ',,,,,..,! ,. (06Marks)

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Fig.Q.2(c) find mass m if the system has a natural frequency ofFor the system shown inlOHz.Take kr :2 N/mm

kz:1.5 N/mmkl :3 N/mmk+: ks:0.5 N/mm.

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3 a. Show that the ratio of successive aqmlifiilks of mass in a underdamped, viscously damped

spring-mass system is given by*o-"u where a=sg;x, Jt-4'

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frg is mounted on a springb. A machine of mass 2f is mounted on a sprifig ffi dashpot. The spring stiffiress is

10 N/mm and damffigis 0.15 N/mm/s. If the mas$l Srinitially at rest and a velocity of100 mm/s is impor.fid"'to it, determine: i) displacement anf,lblocity of mass as a function oftime; ii) displaffint and velocity when time is equal to one$Eond. (10 Marks)

'"Y"r" *ua. Derive pf#*pression for steady state amplitude of vibration ofgaps in a spring-mass-

dampffi$tem when the mass is subjected to harmonic excitation. Also find the phase angle

bet\r€dfl the mass and excitation. " W (10 Marks)

b. A,ftffiratorybody of mass 150kg supported on springs of total stiffnesi lQBp_l<N/m has a

a*Ndtating unbalance force of 525 N at a speed of 6000rpm. If the damping ffi,,gt is 0.3,determine: ""

ii) Transmissibility ratio and '

iii) Force transmitted to the foundation. (r, *".u.1 .,,*

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PART * B5 a. Explain the principle of working of

i) Vibrometer (seismometer) ; ii) Accelerometer. (10 Marks)

b. A rotor of mass 9.5kg is mounted on a 12mm horizontal steel shaft midway between- bearings that are 0.6m apart. The mass centre of the disc is 6mm from its geometric centre.

If the damping factor is 0.1 and the shaft rotates at 690 rpm, determine the maximum stress

in the shaft and compare it with the dead load stress in the shaft. For steel shaft take

E :1.96 x 10rrN/#.2 of3

(10 Marks)

6a.b.

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Explain the principles of dynamic vibration absorber. Derive the necessary equations.(10 Marks)

For the system shown in Fig.Q.6(b) find the natural frequencies and amplitude ratios. Givenm1 : 10kg, m2 : 15kg and k: 320 N/m. (10 Marks)

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b. torsional system(10 Marks)

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Explain the role of i) Exciter; ii) Transducer; iii) Signal conditioner andused in experimental modal analysis.Describe the three types of maintenance schemes given below:i) Breakdown maintenance.ii) Preventive maintenance.iii) Condition-based maintenance.Explain briefly the following methods of condition monitoring:i) Wear debris monitoring.ii) Vibration analysis.

iv) A$5|yzer,(10Mm.,

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Usrng Stodola's method, deJ@e theshown in Fig.Q7(b). ,.1,,.-,

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