Biju Patnaik University of Technology 2008-5th Sem M.C.A Quantitative Technique-II - Question Paper

<! Drftorcriiatoi    cio&od ana op*n

ftyf&ryi

(mi) What oo you ">*ar. Dy a*ayi-ca' 3-3 numerical models ? Ar tey ^r,ta''- dynamic *n naiL*#

(*v) E*j*ars boC' txA*ng pnrote r> modetng

(v) xpfatn congruence random oyt>or gwdalot V/hiii itypc of proWoms you wt'I encounter in this generato* ?    2

fvij What do you moan fcjy infi?r-arrival t'Ufl/I and mean arrival ral m a oucumg System ? Jn which way they Ar rotated ?

(vii)    Explain ASSIGN block *n GPSS

(viii)    What are ihe different operations usod in GPSS programming ?

(ix)    What do you mean by autocorr elated observations ? Give ono example,

<or slimtnaiiori ₀₍ I'an*nis m a oowce of obscrvano 'I >**, er_W, _{typea Q( o( a}

system w.in iheir char8cte_{f(lcs 5}

* '-ame ,hr_6e pnocpa, _om,_es. _attnbutes

^arKl ****** l be corded ,t _you

WO IO simulate rhe operation of petrol fi(|*ng st_alK3n

<&> 3i collee house.    _c

s

l.it Draw itie now chart _{of the process} Qf

SimuJafton E*pla.n tine By ihe important

functions involved    _E

o

Find the correcl value of the constant A that makes the following equation in y, a probability density function. Derive formula for generafjog random numbers having this distribution and compute first five values.

y - A sinx if Os x * k(2 0    otherwise 5

{aj    rfivonie    *<1

for grating faroomnwrtifl Fra

random nvtrmtm co?e*poodrn to t*o

lattowQ pfOto!- ¹V (U'Wi jSirig inverse TrarsJomvalv * rrrty&G

j# 0 ' - * * ' 2 OpMfvvnQ    5

<t>l Describe Monte Oaf to Jecre to evaluate lhr? integral

IWL

(a) The occurrence of rain is dopendeni upon whether rl rained on the* previous day If ft¹ rained on the previous day. Che ram distribution! us given Oy    5

M¹ ?? (JkJ OCX ra*n the previous day. the ram distftbutroo rs given by .

Ev?3

Simulate the city's weather for io days arx# detemime by simulation the total days wishes ram as welt as the total raintai dunng the penocf. Use the foJfow-mg random numbers ;

6.7 633$ 55 29 78 70 0$ 7B 75

A company trading jn motor vehicle spares wishes to determine the level of Stock ii should carry lor the rtems in Its range The demand is not certain and there js a lead time for ihe stock replenishment For one item X, the following mifornation is obtained :    5

DsmarKJ    : 3 4 5 6 7

(Units per day)

Probability ; (XI 02 0.3 0.3 0.1

Canytog eosf po' urnH ifw* day ² 20 pn?5c OrtkKlfrg CDS! JX?f rtMltfr r RsS'-Lead to" wp!smshrH;fi' 3 dayf

S'Gc-. >r f;an<1 in If he b&gfnrurg q* Simuiaijoni rc*r/^fase was 20 ufti are required to cafv Ot/t a Simula Non run over a, period of 10 days w*th lhc objee-itvo of evaluating tfk?¹ floflowmrji iFnvfjntofy rute

Order 15 umis when pfosenr r vr.i p(us any outstandtng ordw tells he*ovv unrts Use the fallowing random; numbers 0. 9. 1. 1. 5. 1, 8, 6, 3. 5

6. (a) The aimval of customers and service rime of customers are havmg tho following distributions. Simulate this quoting system for 10 periods by using the knowing random numbers and calculate ihe mean wailing lime and mean queue length, PMC 5905    5    Contd.

62, 14. 14. 62. 62. 10. 55. 14

Rartdomi numbers for secvtces * 34 35 3.1, 62_t 43. 73 S8. 70, 19. 40. 5

tt?> A bakery keeps stock of a popufaf brand at cake Daity demand based¹ on the past experience is given below ;

Daily dorrmnd 0 10 20 30 40 50 Probability 001 O.tO 023 0.45 0.17 Q.<M Considering the following sequence of random numbers 38* 72, 17, 48_t 53, 78,

11. 16, 65, 07 simulate¹ the demand for the next 10 days.    5

It?    * **9

t4otA 5-    OS-S "^? WV*\! a nr- Tfts

ms\ &    : *-n *

pnft(fitl "* AJsO

ttvy iii%#

IA&JLAJ& GAaT, OtAT *>

40) Wrio a GPS5 fsrogri/n *o? tft* k*3 protHom

.,IWL

Worker! COm 10 A tvWtf IfiVr* raig of ono ovety$ * 2' ifrwHrtf'*. Tfto* nKjutWKX* ar DfOCOfrSed Ibv 00 <* t*C cterkl Wt>0 taka ^Jfi X 4 ffUnulofti tfflr WACh requisition*, Tho roqureiiton* aro ffyn passod to a si'ngta tlcw e keopot who frtfc them ono ai timo. taking A i 3 rrvnulos fo PMC 5905    Q    ContdJ

StiHAtifl l?e iquovrt q|

^lti** * ^,(* /oowwkx* *, b.

ftEai

5

m What rue ftecess.Ty <* reducing the

m * nmuat.on e_Wnfn#0( ?

Ooscnb* LV art.m** sampling _a **Wco i mAjction tact****    5

**> ^A    o* 500 obswvaborts were

₍*nd! fauno 10 be Mnaly correlated. atocotroJaiion coefficients were esnmaion os f₁ = 0 31, 0. 22 and * 012 others are not Significantly difiofoit from zoto The rngan and variance ol 500 samples wete found to bo 22 5 and 980 respectively. Calculate 5905    9    _pT0