# Times Series with Trend & Seasonality

Times Series with Trend & Seasonality

In the two problems here, you may use either Excel’s Data Analysis tool (available only in Windows) or LINEST function to find the regression coefficients. All work must be shown.

D

Hudson Marine has been an authorized dealer for C&D marine radios for the past six years. The number of radios sold each quarter is shown in the Excel template. Hudson Marine would like to forecast the quarterly sales for year 7.

(a) Construct a time series plot.

(b) Construct a multiple regression model with dummy variables to develop an equation that takes into account both trend and seasonality. Give the quarterly forecasts for year 7.

(c) Out of four quarters of the year, which quarter has the peak demand? Which quarter has the lowest demand?

Ch. 7 Linear Programming Formulation

A.

The Outdoor Furniture Corporation manufactures two products, benches and picnic tables. The firm has two main resources: its carpenters (labor force) and a supply of redwood for use in the furniture. During the next production cycle, 1,200 hours of labor are available under a union agreement. The firm also has a stock of 3,500 feet of good-quality redwood.

Each bench that Outdoor Furniture produces requires 6 labor hours and 12 feet of redwood; each picnic table takes 9 labor hours and 40 feet of redwood.

Completed benches will yield a profit of $10 each, and tables will result in a profit of $20 each.

(a) Let B = number of benches to produce and

T = number of tables to produce.

Write down the linear programming model to decide how many benches and tables should be produced to obtain the largest possible profit. Don’t attempt to solve the problem.

(b) Is B = 70, T = 70 feasible solution? How about B= 70, T = 60?

(c) Given an example of a feasible solution that yields total profit of at least $2,000. (There are many such solutions, just give one.) Decimal numbers are OK. The person(s) who gets the highest profit will get 1 extra point on this homework.

B.

Alpine Attic is the charity sponsored by local churches in Denver, Colorado. Literally thousands of items, including televisions and stereos, are donated each year, most in need of repair. Repaired televisions and stereos typically sell for $50 and $30 each at the Alpine Attic Thrift Store. To repair these, Alpine Attic depends on John Lucas who owns JL Electronics, a deacon at St. Paul’s Episcopal Church. Each month, he can donate 45 hours of an electrician’s time and 30 hours of a technician’s time. But this is not enough time to repair all of the televisions and radios donated.

To repair a television, it takes average of 90 minutes of electrician’s time and 30 minutes of a technician’s time.

To repair a stereo, it takes an average of 45 minutes of an electrician’s time and 60 minutes of a technician’s time.

Alpine Attic would like to determine how to best use the electrician’s and technician’s time to realize the maximum possible profit from the donated televisions and stereos. Write down a linear programming model to decide how many televisions and stereos should be repaired each month. Do not attempt to solve. Don’t forget to define the decision variables first.

Hudson Marines

Data & Computation

Year Quarter Sales (units)

1 1 12

2 20

3 17

4 9

2 1 16

2 28

3 25

4 14

3 1 21

2 30

3 27

4 20

4 1 24

2 36

3 30

4 23

5 1 26

2 38

3 32

4 22

6 1 30

2 42

3 37

4 29

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43.

Marketing Research Final Exam

1. As the first stage of a comprehensive physician-satisfaction study, a hospital wants a market researcher to interview about 20% of its 100 physicians. There is known to be quite a bit of animosity between primary care physicians and specialty physicians, as well as between physicians with less than five years of tenure with the hospital and those with five or more years of tenure. Recommend a qualitative analysis technique and give reasons for your selection.

2. You have just conducted a set of focus groups for a client, and the results are positive about launching a new product. Respondents in the focus group overwhelmingly say they will purchase the product. The client is very excited about the results. What words of caution would you give the client before they make this multi-million dollar decision to launch the product? What advice would you give the client?

3. Distinguish between quantitative and qualitative research, especially with respect to the appropriateness of each.

4. How and why would you respond to the following statement: “Advertising and sales are almost perfectly correlated, as when more is spent on advertising, sales go up, and vice-versa. Surely our advertising expenditures are ‘causing’ sales to rise.”

5. You wish to complete 300 phone interviews. Using a random-digit sample, you can expect your working phone rate will be only about 60 percent. How many calls will you likely have to make to achieve your desired interviews?

6. Illustrate a condition in which a “SKIP PATTERN” is needed in a questionnaire.

Given the Correlation Matrix below, answer the following:

AGE INCOME EDUCATION

AGE 1.00

.000

400 -.65

.000

400 -.10

.221

400

INCOME -.65

.000

400 1.00

.000

400 .62

.000

400

EDUCATION -.10

.221

400 .62

.000

400 1.00

.000

400

Assume that respondents answered the questions with ratio scale responses

7. How would you interpret the relationship between Education and Age? Which relationship in the matrix is strongest? How many pairs of responses were in this correlation analysis?

8. When and why does sampling error occur? If the sampling error emanates from some type of improper execution of the sampling plan what is it called? Can it be measured? What kind of sampling error can be measured and how can it be reduced?

9. Compare and contrast the conclusions and recommendations portions of the research report.

10. An advertising agency has been doing work for a client selling widgets. The three-month campaign has produced a low correlation between advertising expenditures and sales for its client. Hence, the client is considering firing the ad agency. The ad agency counters that consumer sales are not a fair assessment of the effectiveness of the ad campaign after only three months. They counter with an analysis of advertising expenditures in relation to number of requests for information about the widgets; number of distributors stocking widgets; and number of retailers requesting shipments of widgets. The ad agency has a database with such information. What kind of analysis would best assist the ad agency in making their case for the effectiveness of their ad campaign? Why?

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