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Unformatted text preview: ISEN 316 TEST 1 2—26 WHITE Instructions: Use the front of your solutions papers only. Place the exam on top of your
answers and staple them together in the left top corner. Write your name and UIN on the
top of this sheet. 36 points I I. Consider an experiment where two die (a pair of dice) (red and blue) are tossed
simultaneously. Both dies are 6 sided with equal areas (equal probabilities of each side
ending up on the top). The red die, however, is unusual in that it has two sides With 1’s
and two sides with 2’s, one side with a 3 and one side with a 4 (these are numbers or dots,
whichever you want to consider). (a) What is a sample space for this experiment (deﬁne it, since there is more than
one way of doing this!) List all the outcomes. (b) How many events are there for this experiment. (c) What is the event that the sum of the top faces equals 4. That is, what are the
outcomes that make up this event? (cl) What is the probability of the event of (c) occurring? 36 points .
2. Consider a E2 / M I 2/ 4 system, with a mean arrival rate of it and a mean service rate per machine of p . (a) Deﬁne a statespace to represent this system probabilistically. (b) Draw the rate—based statediagram of the system (connecting the system
states).   (c) Develop the steady—state equation relating the state probabilities by isolating
on the state where the system is ﬁll] and the arrival process is in the second phase. (d) Write the equation (using the state probabilities) for the WIP in the system. 28 points
3. Consider two workstation serial factory as depicted by the diagram below:  Compute the factory cycle time, throughput and workin—process. Assume the
following data is known: ' ' 21 =Sjobs/hr
C§(1)=2
E[S,] =1/7 hrs
C2[Sl]= 1.5
E[Sz]=10 min
C2[Sz] =3 10 points bonus
4. Deﬁne the following terms: (a) Little’s Law
(b) Utilization (c) Steadystate probabilities .Sxambxesplace *3" (11¢ on Red qfe I 1% on blue Ed‘fe‘g , {C M09031), (1.3), mm, H.933, (Mex
(233, (1(2)) (2133, C2,H7,<2,5‘>, (2,67,/
(3,0, (3,2), (33"), (3m, (3,5),(3gm
mm, (m, (4,3); Mm, (mm (mg/g @ E.1)M/2/L! svswem
A. M 1:114 “W
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7 K: \OR2 L.) n: 4¢ gaps ‘m svs+em
n: 0,1,23H / (MWZP. "
J I J (27%y'p2g coo I ICWe—Hme 2?: +hROUQh§3W€E WORk‘m“PROC€SS: 3
N: 5 calm? EESA= V7 Czisﬂﬂb
£92]: V6 M92313 * I woRkS‘ra'f‘f’O’D 1:
__ v '2’ ’2, _, .
CTS—(Ca +CS) t[sj+E[S] 7.
Ca“(n=2
=C1ESJ:\°5
U: AEESJTSW/Tﬁsh
..'t ‘
63:34?“ 1/5 5// L” /
' 5 I 7: a 7 ‘I+\
w ( ,2 )(Wh/T /—, cTsmz (19763005.) (m +l/7
chm: 05167857 = L43/593. WkPm': )\CTS
;5(q3/56)_ : 3.3301 2 “5/56 GEM]: C121 :2 (HF) 63+ LEG[sf]
_ 01d ‘ 045/717") (“13+ (5/751057
624 = 09m 50: :2 0.1653
C3: LT—Hq /  +  MS EfSﬂ=’/s vim:3 C§=Czofm=L7LIl~lcf CTS: (caHCsZ) His] + Eli's] ‘2
Us: Mm]: 5(t/e‘)= 5/6
./ t/ / ‘a/
CT (2): I:qu +3 5/6 1 \/
S ( '2_ >(i’3/CD /G+ G 7 . CTsm‘): Maggy/“Vs
CTSCZW': 2.1% ~ W IP (23‘: A 073(2) 3/
=5(2M‘)= 20.72 *%g
W‘Psvw WW3er WHM’)
‘5 3w83Cf‘1'iOJ2
= H.559
Cycle+fme= m _ M550: .. 75.7%
A 5 , +hr20ughpu+ = 5
WORKanpﬂocess : H9559 @ LT++ke‘s Law: WoQk— Twmocess = Gt—hs‘zoughpuﬂ MCVQWTWQ
' / @ uﬁlfzaﬁoni
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