Posted: February 8th, 2015

Quantitative methods in business

Quantitative methods in business

Project description
All of the assignments are related to chapter 3&5.
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Added on 06.02.2015 03:02
https://shesclibrary.files.wordpress.com/2013/02/quantitative-analysis-for-management-render-stair-hanna.pdf
This is the link to the book.

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:

NO TRAFFIC?CONGESTION?(minutes)    MILD TRAFFIC?CONGESTION?(minutes)    SEVERE?TRAFFIC?CONGESTION?(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    0.2    0.8
(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

5-42. The gross domestic product (GDP) of the United States from 1993 to 2003 is given in the table below. The numbers are in billions of U.S. dollars. Develop forecasts for the GDP of 2004 using exponential smoothing with smoothing constants of 0.4 and 0.6. Assume the forecast is $6,657 for 1993. Which of these models has the lowest mean absolute deviation?

Year    GDP ($Billions)
1993    6,657
1994    7,072
1995    7,398
1996    7,817
1997    8,304
1998    8,747
1999    9,268
2000    9,817
2001    10,128
2002    10,487
2003    11,004

5-43. Using the GDP data in problem 5-42, develop a trend line for forecasting GDP in the future. Use this to forecast GDP for 2004.
5-44. Jerilyn Ross, a New York City psychologist, specializes in treating patients who are phobic and afraid to leave their homes. The following table indicates how many patients Dr. Ross has seen each year for the past ten years. It also indicates what the robbery rate was in New York City during the same year.

YEAR    NUMBER OF PATIENTS    CRIME RATE (ROBBERIES
PER 1,000 POPULATION)
1    36    58.3
2    33    61.6
3    40    73.4
4    41    75.7
5    40    81.1
6    55    89.0
7    60    101.1
8    54    94.8
9    58    103.3
10    61    116.2

Using trend analysis, how many patients do you think Dr. Ross will see in years 11, 12, and 13? How well does the model fit the data?
5-45. Using trend analysis for the data in problem 5-44, predict the crime rate in years 11, 12, and 13? How well does the model fit the data?
5-46. Using the data in Problem 5-44, apply linear regression to study the relationship between the crime rate and Dr. Ross’s patient load. If the robbery rate increases to 131.2 in year 11, how many phobic patients will Dr. Ross treat? If the crime rate drops to 90.6, what is the patient projection?
5-47. Smith Savings and Loan is proud of its long tradition in Apopka, Florida. Begun by Laurie Shader-Smith thirteen years after World War II, the S&L has bucked the trend of financial and liquidity problems that have plagued the industry since 1988. Deposits have increased slowly but surely over the years, despite recessions in 1967, 1972, and 1987. Ms. Shader-Smith believes it necessary to have a strategic plan for her firm, including a one-year forecast of deposits. She examines the past deposit data and also peruses Florida’s gross state product (GSP) over the same 44 years. [GSP is analogous to gross national product, (GNP) but on the state level.]
Using exponential smoothing with a = 0.6, predict deposits for 2003. Assume that the forecast for 1959 was 0.25. Compare this model with an exponential smoothing model with a = 0.2. Which model is better?

YEAR    DEPOSITS    GSP
1959    0.25    0.4
1960    0.24    0.4
1961    0.24    0.5
1962    0.26    0.7
1963    0.25    0.9
1964    0.30    1.0
1965    0.31    1.4
1966    0.32    1.7
1967    0.24    1.3
1968    0.26    1.2
1969    0.25    1.1
1970    0.33    0.9
1971    0.50    1.2
1972    0.95    1.2
1973    1.7    1.2
1974    2.3    1.6
1975    2.8    1.5
1976    2.8    1.6
1977    2.7    1.7
1978    3.9    1.9
1979    4.9    1.9
1980    5.3    2.3
1981    6.2    2.5
1982    4.1    2.8
1983    4.5    2.9
1984    6.1    3.4
1985    7.7    3.8
1986    10.1    4.1
1987    15.2    4.0
1988    18.1    4.0
1989    24.1    3.9
1990    25.6    3.8
1991    30.3    3.8
1992    36.0    3.7
1993    31.1    4.1
1994    31.7    4.1
1995    38.5    4.0
1996    47.9    4.5
1997    49.1    4.6
1998    55.8    4.5
1999    70.1    4.6
2000    70.9    4.6
2001    79.1    4.7
2002    94.0    5.0

Note: Deposits in millions of dollars, GSP in billions of dollars.
5-48. Using exponential smoothing with a = 0.6 for the data in problem 5-47, predict GSP for 2003. Assume that the forecast for 1959 was 0.40. Compare this model with an exponential smoothing model with a = 0.2. Which model is better?
5-49. Using the data in problem 5-47, develop a trend line and predict deposits in 2003, 2004, and 2005. Develop a trend line and predict GSP in 2003, 2004, and 2005.
5-50. Using the data in problem 5-47, develop a regression line to predict deposits based on GSP. Examine the data carefully. Can you make a case for excluding a portion of the information? Why? ??