Homework 1
3-53. Chris Dunphy, executive vice president for marketing and sales of Sumu Electronics, is considering the possibility of introducing a
new line of inexpensive wrist watches, which would be oriented primarily toward young adults. The watch would have a plastic faceplate
and wristband and a variety of features, including an alarm, a chronograph, and the ability to store and retrieve various split times. The
watch has been designed to come in a variety of colors and styles. The retail price of the watch is expected to be $19. At this price, Chris
feels that there is a substantial market for the watch. To help gain further information, Chris has hired a marketing research firm to study
the market potential for this new venture.
The marketing research team conducted a survey and a pilot study to determine the potential market for the new watch being considered
by Sumu. The team, realizing that there is market risk associated with any new product, looked at the potential market on a five-point
scale, the marketing research team looked at a variety of production, or stocking, policies related to each of the marketing segments. The
stocking policies involve producing 100,000 to 500,000 watches.
The worst market scenario for Sumu was still expected to bring profitability through all stocking ranges. (Remember, the worst-case
marketing scenario was assigned a value of 1 on the five-point scale.) The probability of having a 1-type market was estimated to be 0.10.
A stocking policy of 100,000 units was expected to return a net profit of $100,000 for Sumu. A stocking policy of 150,000 units was
expected to return only $90,000. Similarly, higher stocking policies for a market potential of 1 were expected to yield lower profits. A
stocking policy of 200,000 was expected to return $85,000 in net profits. The stocking policies of 250,000, 300,000, 350,000, 400,000,
450,000 and 500,000 were expected to yield net profits of $80,000, $65,000, $50,000, $45,000, $30,000 and $20,000 respectively.
The next-best market scenario was categorized by the number 2. This market potential was categorized as below average and the
marketing research team estimated that the chance of getting a below average market was 20%. The net profit for the beginning stocking
policy of 100,000 units was estimated to be $110,000. The net profit for stocking 150,000 units was $120,000. If Sumu stocked 200,000
units, the net profit would be $110,000. A net profit of $120,000 would be realized if the stocking policy was 250,000 units. Stocking
policies of 300,000, 350,000, 400,000, 450,000, and 500,000 would result in net profits of $100,000, $100,000, $95,000, $90,000, and
$85,000 respectively.
The marketing research team estimated that the probability of an average market was 50%. This average market was coded with a 3 on
the five-point scale. In general, profits were significantly higher for all stocking policies with this average market scenario. As before,
profitability figures were estimated for all the stocking policies, ranging from 100,000 to 500,000 units. The net profitabilities for this
range are $120,000, $140,000, $135,000, $155,000, $155,000, $160,000, $170,000, $165,000, and $160,000.
A good market potential for the watches was given a 4 on the five-point scale. The probability, however, of a good market was relatively
low. It was estimated to be 10%. Net profitability factors for stocking policies that range from 100,000 to 500,000 units were estimated to
be $135,000, $155,000, $160,000, $170,000, $180,000, $190,000, $200,000, $230,000 and $270,000.
The probability of a very good market was estimated to be 10%. This market received a 5 on the scale. Probability factors for this market,
in general, were higher. The profitability factors for stocking policies that range from 100,000 to 500,000 were $140,000, $170,000,
$175,000, $180,000, $195,000, $210,000, $230,000, $245,000, and $295,000.
(a) Determine the expected monetary values for each of the stocking policy alternatives.
(b) Which stocking policy do you recommend?
(c) What is the expected value of perfect information for this situation?
(d) Chris has just received information that the original probability estimations were not accurate.
Market 2 has a probability of 0.28 while market 5 has a probability of 0.02. Does this new information change any decision?
Chris has also received new information about stocking 500,000 watches. The return given a very good market is now estimated to be
$340,000. What is the impact of the new probability values [given in point c] and the new return for a very good market for stocking
500,000 units?
3-54. Helen Murvis, hospital administrator for Portland General Hospital, is trying to determine whether to build a large wing onto the
existing hospital, a small wing, or no wing at all. If the population of Portland continues to grow, a large wing could return $150,000 to
the hospital each year. If the small wing were built, it would return $60,000 to the hospital each year if the population continues to grow.
If the population of Portland remains the same, the hospital would encounter a loss of $85,000 if the large wing were built. Furthermore, a
loss of $45,000 would be realized if the small wing were constructed and the population remains the same. Unfortunately, Helen does not
have any information about the future population of Portland.
(a) What type of decision problem is this?
(b) Construct a decision table.
(c) Using the equally likely criterion, determine the best alternative.
3-55. Hardie Lord, Helen Murvis's boss, is not convinced that Helen used the correct decision technique. (Refer to Problem 3-54.) Hardie
believes that Helen should use a coefficient of realism of 0.75 in determining the best alternative. Hardie thinks of himself as a realist.
(a) Develop a decision table for this problem.
(b) Using the criterion of realism, what is the best decision?
(c) Did Hardie's decision technique result in a decision that was different from Helen's?
3-56. Dorothy Stanyard has three major routes to take to work. She can take Tennessee Street the entire way, she can take several back
streets to work, or she can use the expressway. The traffic patterns are very complex, however. Under good conditions, Tennessee Street is
the fastest route. When Tennessee is congested, one of the other routes is usually preferable. Over the past two months, Dorothy has tried
each route several times under different traffic conditions. This information is summarized in minutes of travel time to work in the
following table:
SEVERE
NO TRAFFIC MILD TRAFFIC TRAFFIC
CONGESTION CONGESTION CONGESTION
(minutes)
(minutes)
(minutes)
Tennessee Street 15
30
45
Back roads
20
25
35
Expressway
30
30
30
In the past 60 days, Dorothy encountered severe traffic congestion 10 days and mild traffic congestion 20 days. Assume that the last 60
days are typical of traffic conditions.
(a) Develop a decision table for this decision.
(b) What route should Dorothy take if she wants to minimize average drive time?
(c) Dorothy is about to buy a radio for her car that would tell her the exact traffic conditions before she started to work each morning.
How much time in minutes on the average would Dorothy save by buying the radio?
3-57. After buying a computer system, Sim Thomas must decide whether to purchase (1) a complete maintenance (or service) policy at a
cost of $500, which would cover all maintenance costs; (2) a partial maintenance policy at a cost of $300, which would cover some of the
costs of maintenance; or (3) no maintenance policy. The consequences, costs and probabilities are given in the following table:
MAINTENANCE
REQUIRED
NOT REQUIRED
No Service Agreement
$3,000
$0
Partial Service Agreement
$1,500
$300
Complete Service Agreement $500
$500
Probabilities
0.8
0.2
(a) What do you recommend?
(b) If the probability of needing maintenance is 0.8 (instead of 0.2) and the probability of not needing maintenance is 0.2, how does this
change Sim's decision?
3-58. Bob Welch, a famous divorce attorney, is facing a decision with four options (alternatives) and four scenarios (states of nature). The
options relate to furniture in his client's house. The options range from a cash settlement for the furniture (Options 1) to aggressively
litigating the issue (Option 4), where his client could get $30,000 or suffer a $20,000 loss from fees and related costs. He does not know
the probabilities of the states of nature, which include Scenario 1 (favorable judge), Scenario 2 (jury trial), Scenario 3 (out of court
settlement), and Scenario 4 (arbitration). (See the following table.) Help Bob by determining the maximax and maximin decisions. What
is the equally likely decision?
SCENARIO 1 SCENARIO 2 SCENARIO 3 SCENARIO 4
Option 1 $5,000
$5,000
$5,000
$5,000
Option 2 $10,000
$5,000
$2,000
$0
Option 3 $20,000
$7,000
$1,000
-$5,000
Option 4 $30,000
$15,000
-$10,000
-$20,000