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Unformatted text preview: ARE 157 NAME: 904W MIDTERM 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. 307 Part A. 10 points each. 1. Trevor works for a glass manufacturer. He has sampled the temperature of a vat of molten glass
and found that it has a mean of 202 degrees and a sample standard deviation of 1 degree. The
manufacturer has set a target temperature of 201 degrees, with an upper speciﬁcation limit of 204
and a lower speciﬁcation limit of 198. What does he conclude? a. The process is operating satisfactorily. b. The process is not capable of staying in tolerance © The process is likely to produce glass that is too hot.
d. The process is likely to produce glass that is too cool. 2. The supply chain for the US beef industry has changed location over time. How would you
describe these changes?
a. Feedlots and slaughterhouses have moved closer to consumers’ locations
® Feedlots and slaughterhouses have moved closer to cattle producing regions
c. Cattle ranchers have moved closer to consumers’ locations
(1. Cattle ranchers have moved closer to major livestock terminals such as Omaha, Denver
and Chicago. 3. Each day, Michelle sampled 16 units of output from a packaging machine, and developed a 3
sigma mean control chart from the results. The population standard deviation of the process is
known to be 6 = 2. Over the past 4 days, the sample means have been 90, 91, 91, and 92. What
statement below is consistent with these results? a. The upper control limit is 97. @The lower control limit is 89.5
c. The process is out of control.
d. None of the above. 4. Which of the following would tend to smooth a weekly data set the most?
10week simple moving average
b. 3week weighted moving average with weights .6, .3, .1
c. exponential smoothing with alpha = .8
d. exponential smoothing with alpha = .2 5. Conrad used two forecasting models to predict auto sales. He later evaluated the models and
found the following:
Model A: mean squared error = 40; mean absolute deviation = 6; mean forecast error = +3
Model B: mean squared error = 50; mean absolute deviation = 7; mean forecast error = 2
What do his ﬁndings imply?
a Model A has a positive bias.
b. Model B has a better goodnessofﬁt
0. Both a and b.
@Neither a nor b. 6. Sarah would like to remove the seasonal effects from her firm’s monthly sales data. Which time
series technique below would be useful for this purpose?
a. 12month moving average
b. Time series decomposition
@ Either a or b would be useful.
(1. Neither 21 nor b would be useful. 7. What event below is likely to lead to cyclical demand for goods in the future?
Year of the Pig in China
b. Easter holiday in the United States
c. Both a and b.
(1. Neither a nor b. 8. Which of the following types of services would most likely be classiﬁed as “low complexity,
customized?”
a. Retail giﬁ shop
b. Symphony orchestra
c. Dentist
@Lawn mowing service 9. Which of the following best agrees with Dr. Deming’s ideas regarding quality improvement?
3. All items should be inspected before sale to ensure there are no defects.
@ Statistical sampling should be used to ensure that output is consistently of good quality.
c. Job duties should be deﬁned narrowly, so that workers can master their speciﬁc tasks
better.
d. All of the above. 10. What is the advantage of a maketostock approach in manufacturing?
a Lower inventory costs
6) Faster fulﬁllment of customer orders
c. Allows for customization of the product
(1. All of the above 11. Costs of quality include prevention costs, appraisal costs, internal failure costs and external
failure costs. Which of the following is an example of an internal failure cost?
a. Lost sales due to firm’s reputation for poor quality
b. Cost of testing items for defects aﬁer they have been produced but before they are sold.
©Cost of repairing items found defective before they have been sold.
d. Cost of training employees to avoid mistakes in production process. PROBLEMS (40 points each) Show your work! Partial credit given.
1. A ﬁrm’s manufacturing plant operates on a 450minute shift, and is designed to produce 90 units
per shiﬁ. Assembling the units requires completing seven tasks. Each task’s required time and
predecessors (if any) are listed below: Task Time re uired (minutes) redecessors (4).a. What is the maximum cycle time for this process? V\‘> I 3"“ C l _, g (WW q 0 upwi‘slsluii w W}
DVD CLUUU (24). b. Using the line balancing approach we applied in class, assign each task to the appropriate
workstation, and show the time required at each station. Sta owl: wa’laloﬂo, (1 L Mailabic 0.19,) (i; whim wwl.%~ﬁmm \gﬂ
(6)0. What is the idle time per cycle? : ESE] 0 +03 to +01 : 15mm! (6)d. What is the percent line efficiency? a} X [We 3
Li (Li Kl ) 2. Samantha plans to insure her office building against ﬂood damage. She believes that each year,
there is a 2% chance of a major ﬂood that will cause $300,000 of damage, and a 4% of a minor ﬂood that will cause $100,000 of damage. She is considering 2 policies:
Policy A costs $10,000/yr. It has a $20,000 deductible, and pays for 90% of any remaining damage above that amount.
Policy B costs $12,000/yr. It has no deductible, and pays for all damages. Develop a decision matrix that shows: the actual outcomes under each state of the world; the
expected value of each policy, and the standard deviation of outcomes under each‘policy. F 3. HiHat Products produces cymbals. The ﬁrm is considering leasing new machines for its
production plant. There are two different models of these machines that are being considered. Each
has a ﬁxed monthly lease cost, plus variable costs that depend on the number of units produced, as
follows: Model A’s cost function per month is TCa = $640 + 6*qa + 0.1*qa2
Model B’s cost ﬁmction per month is: TCb = $1000 + qu + 0.1“qb2 a. (20) What is the most costefﬁcient level of output for each model of machine? (That is, what
are qa* and qb*?) Aﬂtffl’lC beg:0 +1hI ﬁvb’hz‘m _,_....
%', SEQ) , 1.4th b. (10) What is each model’ 3 average total cost, assuming it is operated at its optimal level from art a? I I ‘ o
All“: 5+ 4; +..l(%): elkawn! 22 Wwwr c. (10) Suppose the ﬁrm requires an output of 400 cymbalsﬂper month. Which model of machine
should it choose, and how many machines should be used? Given this choice, what is the ﬁrm’s average total costper unit for roducin cymbals?  ; W WM “’3 “Ml \Wm... WWW—— 7‘OY LSM 5 M#£+M:ZEE] {17? MM rt 8 IPA 4. Vincent forecasts sales of washing machines for an appliance manufacturer. During 2006, he
forecast quarterly sales using 2 different models, A and B. Now that actual 2006 sales are known,
he wants to evaluate the 2 models and see which performed better. Actual F’cast A F’cast—B
Spring 2006 82 ' 78 80
Summer 2006 95 94 97
Fall 2006 98 96 96
Winter 2006 83 84 85 (10)a Find the mean squared error (M.S.E.) for each forecast. 4 m 2 j
I l ‘7,
0. H 2. ‘i
~l ‘ «Z. Li
772 MSEPF 2%: 1E VMEB: Li (10)b. Find the Mean Absolute Deviation (M.A.D.) for each forecast. D : 491+z+t e;
m“ A Lf :Q’CE _ z+L+Z+Z 3 _. (10)c. Based on MSE, which model had the better ﬁt? And based on MAD, which model had a beneﬁt? EMORng W00 W (10)d. Was either model biased, and if so, in what direction? H Z~l 5. Suppose Solano County uses a scantronbased votecounting machine to count ballots cast in its
elections. Due to concerns about the accuracy of these machines, the county performs a test on each
machine, as follows. A test set of ballots known to contain 2000 votes for Candidite A is run through the machine 20
times. Suppose that for one of these machines, the results were: 13 times the machine reported 2000 votes
4 times the machine reported 1997 votes
2 times the machine reported 2003 votes
1 time the machine reported 2006 votes. The county supervisor of elections has declared that she will tolerate an error rate of no more than
1/2 of one percent in either direction. Thus the target is 2000, with an USL of 2010 and a LSL of
1990. (16). Find the mean and sample standard deviation of the machine results.
*‘ a L i Z ’20 ‘l 2
X _ 13(20003 “193512) + t 07.)) Doc: C2000}
O 0 ‘73 (20004000? t L‘ 0 9‘1?  2000)2 + 1(2003200077' r (20062m}
10 ‘ l : W: :QOW
W l c] (12) What are the maximum and minimum vote counts that this machine might be expected to
produce, if the same test was repeated many times? )2 + as = 2.00 o + 3(247 episcong {El X o r N D. 00 7
vatwt : En 3s = 61000  Writ»:— Iﬁqgm ;_
. . UV A.) l q q 3
(12). Find the/process capability index, Cp. Is this machine capable of staying in tolerance?
(ML  is" ) f‘ S ’ZOIO 4990 _ .
gnaw 6. . Confab Corp constructs new homes in Northern California. The ﬁrm’s sales over the past 2
years have been: (# of homes sold)
Sales 2005 2006
1st Qtr. 75 60
2“d Qtr. 95 70
3rd Qtr. 1 10 100 80 ~52
Yzﬂmwwiwwz7o a. (12) Predict 1St Qtr 2007 sales, using time series decomposition (additive model).
Wot *1 ‘7 O “C? O t r l9l (Mr S,Q.CLSOYLOJ 73"?0 : ~/§' gov7o : "f"/0 M
—Z§/z : "—4745 4th Qtr. cha/ﬁ’ \Pl‘G‘zW 0’): 7020425: 3’74: l37 1—033’hm'vwo b. (12) Predict 1st Qtr 2007 sales, using time series decomposition (multiplicative model). W 2390 1' {77%
__ 7.5 60 ..
lea“ SJZGLSGYLm/Q ' 90 + jB>/l: 6%q5 Few/cw ls’rcﬁw‘on : 70 Kg??? yfms :T’lL/Cgl . _ . homo: ,
c. (8) Predict 1St Qtr 2007 sales, using a 4quarter Simple movmg average. Go+7o+l00t§0 w t 70 Rom d. (8) Predict 1St Qtr 2007 sales, using a 4quarter weighted moving average with weights . (4, .3, .2, .1). .
614(9)) mum) +02C707+cltec0 ..\7o W ...
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This note was uploaded on 04/13/2008 for the course ARE 157 taught by Professor Whitney during the Spring '08 term at UC Davis.
 Spring '08
 WHITNEY

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