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Unformatted text preview: ARE 157 n P O 5+ FALL 2007 Name: MIDTERM Kw] B (Jam/1‘) Section A consists of l 1 multiple choice questions worth 10 points each. Section B consists of 6 problems worth 40 points each. Please show your work for full credit. If you can't solve
one step of a problem, you can still get credit for the remainder if you use the correct method. Total points possible = 350. SECTION A~ 10 points each 1. Tyrone used two forecasting models to predict sales of his ﬁlm’s cell phones.. Over the past
several ears, the two models have erformed as follows: Mean squared error Mean abs. deviation Mean forecast error What does this information imply about these models?
a. Model X is biased upward
@ Model X ﬁts the data better than model Y
c. Both a and b are true.
(1. None of the above. 2. Lillian purchased ﬂood insurance coverage for a property she owned. The policy cost $1800, had
a $10,000 deductible, and promised to pay 80% of any remaining ﬂood damage. Later that year, a ﬂood caused $200,000 in damages to Lillian’s property. What was her actual
cash outﬂow that year? a. $51,800 $9 $49,800
c. $48,200
d. None of the above 3. In our classroom examples, which ﬁrm below revised its mission statement because it had formerly
been too speciﬁc?
AT&T
b. Pepsi
c. Enron
d. All of the above. 4. Which of the expenditures below would W. Edwards Deming probably most approve of, for an
automaker trying to achieve a high level of quality?
3. Costs of recalling and repairing vehicles that were found to have defects.
® Costs of hiring expert designers to help design new models that are more durable.
c. Costs of inspecting each car before it is sold, to be sure it is free of defects.
(1. Costs of adding luxury features such as moon roofs and leather upholstery. 5. Which of the following goods is known for its cyclical pattern of prices?
a. Eggs b. Swimsuits @ Pork d. None of the above. 6. Which of these historical events began in the United States?
a. The Industrial Revolution
@ Use of interchangeable parts in manufacturing
c. Just—intime inventory management
d. All of the above 7. An accounting ﬁrm is an example of what general type of service operation?
a. Low complexity, standardized
b. Low complexity, customized
c. High complexity, standardized
@ High complexity, customized 8. Donna is in charge of scheduling staff for a large department store. She uses past sales data to
forecast future sales, so she can predict stafﬁng needs during likely busy periods, such as before
holidays. Which time series technique below would be most useful for her? a. Simple moving average b. Weighted moving average. c. Exponential smoothing 61:) Time series decomposition e. All of the above methods would be equally good for this purpose. 9. A production line has the following work stations: (with times shown in minutes) 1 >II—"“""‘">Hla'——v—'~?IV 2.3 2.6\\\ 4.8 / 2.5 111 b
4.8 Which of the following statements are correct?
a. A bottleneck may develop in front of stations 111a and IIIb
b. A bottleneck may develop in front of station IV.
© The actual cycle time will be 2.6 minutes.
d. All of the above. 10. Barry sampled 25 packages of nails from a production line, and counted the nails in each. He
found the sample mean to be 51.5, with a sample standard deviation of 0.7. The ﬁrm requires that its
packages contain at least 50 nails, and no more than 54. What does Barry conclude?
a. The process is capable of staying in tolerance, and is operating satisfactorily.
b. The process is capable of staying in tolerance, but is not operating satisfactorily since some
packages will contain too few nails.
c. The process is capable of staying in tolerance, but is not operating satisfactorily since some
packages will contain too many nails.
.The process is not capable of staying in tolerance. 1 . Julia is analyzing daily sales data for her ﬁrm, Scott Products. Because daily data is highly variable
(“noisy”) she wants to smooth the data before presenting it at a staff meeting. Which of the time series
techniques below would smooth her data the most? a. a 3day simple moving average b. a 3day weighted moving average with weights .6, .3, and .1 @exponential smoothing with alpha = .2 d. all the above techniques would smooth the data equally. PROBLEMS (40 points each) Show your work! Partial credit given for correct method. 1. Giselle works in a factory that produces thumbtacks. One of her duties is to monitor a packaging
machine that produces packages labeled as “100 thumbtacks”. The machine has worked satisfactorily
in the past, so she monitors it using a mean control chart. Every hour she samples 6 packages of thumbtacks and counts them. Here are the results of her
last 4 hourly samples: pkg. hour 1 hour 2 hour 3 hour 4
l 104 103 105 100
2 102 103 103 101
3 102 102 104 104
4 104 104 104 100
5 103 104 103 103
6 1% 1.92 19.5. M
Xbar 103 103 104 102 a.(10) Find the mean of sample means, “Xbarbar”. (Note: the mean of each sample is already shown) :: w3+wa+wv4+mZ
X ‘{ :MOBI b. (10) Find the standard deviation of sample means, 0")? . Assume the population standard deviation
is o = 0.9798. g: .Q798 
“W; r? ”E1 c. (10) What are the upper and lower 3sigma control limits for this prOcess? uu: §+sojz= Ioa+3(.</);/m7
LcL: Wage ms — Z(,V):[/0/,87 d. (10) Is this process in control? Show or explain how you know. I . _  —— , ~— —~> .. UCLCIO ‘
Fﬂ . ‘11 @Wﬁemww »« a ’°""“”'X‘”3
0M Wat/MM 0
MM“! ”ﬂqnﬂﬁ#—ﬁ»*¢~litcmL2 2. Sherman, an art dealer, recently acquired a painting that is said to have been painted by the famous
painter Marc Chagall. However, there is a possibility that the painting is a forgery, painted by an
unknown artist. Sherman is considering having the painting appraised by experts. It will cost $40,000 to have
the painting appraised . If the painting is found to be authentic by the experts, it can be sold for
$840,000. However, if it is found to be a forgery, it will only sell for $10,000. Sherman believes there
is a 40% chance the painting is authentic, and a 60% chance it is a forgery. Alternatively, Sherman has found a buyer who is willing to pay $250,000 for the painting today,
without having it appraised. a. (36) Illustrate this problem in a decision matrix. Show the actual ﬁnancial outcomes that can occur,
and the expected value and standard deviation for each strategy. (Hint: your strategies are “pay for
appraisal” or “sell now”, and the states of the world are “authentic” and “forgery”.) 1)th P:'() EXP UOJAL 0" WW
6: N .Ll (‘3'60000 4mm)" +.c(—3oooo —3o2ooo)z b. (4) If Sherman is riskneutral, what strategy should he choose? /
L a a . 7m gthCQ. EA” > zgolooo
(301,000) 3. Ski World’s sales revenues for the past 2 years are shown below. The ﬁrm will use time series
decomposition to forecast sales for the upcoming year. 2005 2006
Spring , 10 12
Summer 5 7
Fall 85 90
Winter 140 143 P. Y: ZVo/q: éo ZyZ/q: 4; a. (20) Using an additive model, ﬁnd the trend component; the spring seasonal component; and the
spring 2007 forecast. wdlkw
WA 7" 63490 3 [a
Od‘dkt ,
$aﬁvm)s,aasmaﬁ:. Qo—e0\[email protected]"é3)_ ~5’O,S” 2 WWW Maw? = 63 J“ 3 “30's: [’55,] (or [Th/4 1s okay} b. (20) Using a multiplicative model, ﬁnd the trend component; the winter seasonal component and
the winter 2007 forecast. ,. 05
MWW (70' \.
WlKW M F”. 'l‘lo ”13
5166634 —_: _. .— M L604" 973/ : 9'30'4’
Z wo’léﬁ
WMW may”. it“ (as? : ¢3x2,3o/éx/.O§ :W W I»: /92 4. Tom uses recent sales data to forecast future sales at his café. a. (20) Find Tom’s forecasts for weeks 2 and 3, assuming he uses exponential smoothing with
alpha = .2 Assume his initial forecast for week 1 was 940. Week 1 Week 2 Week 3 Actual sales Forecast A1 = 1000 F1 = 940 (given) A2=950 F2= ,1(iooo\+.?LQ‘/O): ligE/ A3=930 F3= ,z(9503+.5’(95ZlZ/9/5’7Té/
or N 7‘5’2 b. (10) What is his Week 4 forecast, if he uses a 3week simple moving average? (Use actual sales
data from above to work this problem). F4= +C130
[0001'ng : 9‘60 3 “ﬂy—u c. (10) What is his Week 4 forecast, if he uses a 3week weighted moving average with weights of .5,
.3, and .2? (Again, use actual sales data from part a.) F4= . 9 (@305 7‘ .3(95‘D\)+ 510000) 1 FE? 5. Tremont Building Supply produces roof trusses. The sequence of tasks necessary to produce each
item, and the required time (in minutes) per task, are shown below. A work shift is 250 minutes long,
and the required output per shift is 25 units. Task Time Predecessors none 250 Wk M a b WWK U1CQLW:M Z§ umB/stqﬂ none
none ': LO WMSl (14/41 
c,d e, f 3 g snow» /
./
./
/
/ / ‘khBUINNGN :QWW a. (28) Using the rule of thumb we learned in class, assign the tasks to work stations. Show which tasks
are done at each station, and the total time needed at each station. QMDI .
Waxing/Q0. Ame MID! 7
mammal Alt; 2 (Eishmlmvj) shin 1T
Time E B ©9me 9 CLUWiCLIQ/QQ. E, )C’ M :8
ﬁfuﬁwvtm ,,
WEI? W5 3 M137 M8 ‘ .1
Swag/3w H b (6) What is the percent line efﬁciency for this line. 070 12%“ : w X /od% :1 34.47% I c. (6) What is the idle time per cycle? Emit/bafﬂe 4C?) “‘ (7Fg7cqu) : 5L 1 6. Brennan is considering two different models of machines for printing sales brochures.
Model A has annual cost function 5000 + 4 q + .02 qA2 Model B has annual cost function 5625 + 5 q + .01 q"2 a. (20) What is the optimal annual output quantity for each model? (The output level for which each
machine’s average total cost is minimized.) ATZ=MC
A' 5:952 + y+ 432%.f = %.0yfﬁt
 A
S’ooo X: €000 : S7’01
: ,0274 gt '01 ~
in
$3 562/31L/g‘; o/ngﬂwL 0276
§é25 5‘0/
5,61% 0/715 66/21/76”; {to b. (10) What is the average total cost (cost per brochure) for each machine, if it operates at its optimal output level? 0 0
Ann: %0 L/+,OZ(S‘UO): {3‘qu nmgzw + 5 +.)01(m z/faol c. (l 0) Suppose Brennan needs to produce 1 500 brochures per year. Which model should he purchase,
and how many machines will be needed? What does it cost him to produce each brochure? Faxed/um lm ...
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 Spring '08
 WHITNEY

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