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Unformatted text preview: ARE 157 Spring 2008
M.Whitney ANALYSIS FOR PRODUCTION MANAGEMENT Homework 1
Due Tuesday, April 15th, at start of class 1. (12) Simon is a quality control inspector for Chico Cookies. He has collected samples of
cookies produced by two of the ﬁrm’s packaging machines, as shown below. The ﬁrm’s cookies are packaged in bags labeled as containing 16 ounces. In order to
ensure that no customers are shorted, the ﬁrm requires that each bag contains at least 16 ounces,
with a target of 16.15 ounces and an upper limit of 16.30 ounces. Machine A Machine B 2 bags contained 16.10 . 1 bag contained 16.00
9 bags contained 16.15 14 bags contained 16.10 10 bags contained 16.20 8 bags contained 16.20
4 bags contained 16.25 2 bags contained 16.25 a. (1) Aﬂer looking at the 2 samples above, Simon’s coworker, Denise, concluded that both
machines are operating satisfactorily, since none of the sampled bags are out of tolerance.
Explain why this is not a satisfactory criterion for quality control purposes. b. (8) Find the mean and sample standard deviation of each sample. What are the largest and
smallest weight that is expected to occur for each machine, assuming a normal distribution? c. (3) Is Machine A operating satisfactorily at present? Is it capable of being controlled? Is
Machine B operating satisfactorily at present? Is it capable of being controlled? Show how you
know. What type of action, if any, should the ﬁrm take? 2. (10) Brad works in a factory that produces buttons. One of his duties is to monitor a machine
that places buttons in packages labeled as “100 buttons”. The machine has worked satisfactorily
in the past, so Brad monitors it using a mean control chart. Every hour he samples 5 packages of buttons and counts them. Here are the results of his
last 4 hourly samples: pkg. hour 1 hour 2 hour 3 hour 4
1 104 103 105 101 2 102 103 103 102 3 102 102 104 104 4 104 102 104 105 5 L0} in m. an
Xbar9103 102 104 103 a. (2) Find the mean of sample means, “Xbarbar”. (Note: the mean of each sample is already
shown) Also ﬁnd the standard deviation of sample means, 0 '2, assuming the population standard
deviation is o = 1.04. b. (4) What are the upper and lower 3sigma control limits for this process? Is the mean of this
process in control? Show or explain how you know. c, (4) How would your answer to part b change, if the ﬁnn’s management decided to implement
2sigma mean control limits? 3. (16) Stanley Ofﬁce Supply is considering whether to purchase ﬂood insurance for its
headquarters building in North Natomas, CA. The ﬁrm expects that in each year, there is a 1%
chance of a major ﬂood causing $3,000,000 in damage, and a 4% chance of a minor ﬂood
causing $500,000 in damage. The ﬁrm is considering 3 options to address this risk: Policy A costs $38,000/year. It has a deductible of $20,000, then pays for 75% of any damages above that amount.
' Policy B costs $42,000/year. It has no deductible, and pays for 80% of any damages. Selfinsure. The ﬁrm pays for all its own damages should they occur. (a) (15) Develop a decision matrix that shows the actual dollar outcomes that can occur for
each of the three options above, and their expected values. Also calculate the standard deviation
for each option. (b) (1) If the ﬁrm is riskneutral, which option should it choose? If the ﬁrm is highly risk
averse (preferring the option with the smallest standard deviation), then what strategy will it
choose? 4. (6) Silveyville Natural Foods is deciding whether to open a second retail store, in addition to
its existing one. The ﬁrm’s projected proﬁts depend on the strength of the overall economy, as
shown below: (numbers are in millions)
economic activi Strong Average Weak expected stande
strategy p=.2 p=.5 p=..3 value deviation
I
" Find the expected value and standard deviation for each strategy. Which strategy should the ﬁrm
 select, assuming it is riskneutral? Would the same choice still be best if the ﬁrm was highly
risk—averse? 5. (6) Find and print out (or copy down) an example of (a) an effective mission statement; and
(b) a poorly designed mission statement. Brieﬂy describe why you think these mission
statements are effective or ineﬁ'ective,. taking into account the 2 criteria we mentioned in class. ...
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 Spring '08
 WHITNEY

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