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Problem 1

Suppose a manufacturing company makes a certain item. The time to produce each item is normally distributed around a mean of 27 minutes with a standard deviation of 2.5 minutes. Thus, the population of production times is normal in shape. Find the mean and standard deviation of the sample.

Problem 2

The average prices for a product in 12stores in a city are shown below.

$2.99, $2.85, $3.25, $3.55, $3.00, $2.99, $2.76, $3.50, $3.20, $2.85, $3.75, $3.85

Test the hypothesis that the average price is higher than $2.87. Use level of significance a = 0.05.

Problem 3

A store wishes to predict net profit as a function of sales for the next year.The following table gives the years 1998 to 2005.

Year

Sales

(thousands of dollars)

Net Profit

1998

51

5

1999

55

10.2

2000

65

9.6

2001

82

-3

2002

75

2.8

2003

71

3.2

2004

82

-2.3

2005

81

-2.6

(a) Graph the points from 1998 through 2005on ascatter diagram using Sales as the independent variable and Net Profit as the dependent variable.

(b) Draw the regression line on the graph you constructed in Part (a).

(c) What is the value of the coefficient of determination for this regression model? Comment on the strength of the regression line for this model.

(d) What is the predicted net profit for 2006 if sales are expected to be 125?

Problem 4

Last week’s sales of iMac computers at an Apple Store in Oklahoma City, OK,are shown in the following table:

Day

Sales (Dollars)

1

180

2

150

3

210

4

225

5

195

6

190

7

230

(a) Use the 3-day moving average method for forecasting days 4–7.

(b) Use the 3-day weighted moving average method for forecasting days 4–7. Use Weight 1 day ago = 2, Weight 2 days ago = 4, and Weight 3 days ago = 3.

(c) Compare the techniques using the mean absolute deviation (MAD).

Problem 5

The following table shows six years of average annual cost-of-living index data:

Year

Annual Cost of Living Index

2008

105.8

2009

111.4

2010

121.9

2011

134.3

2012

128.6

2013

125.2

(a) Forecast the average annual food price index for all years from 2008 to 2013. Use a 3-year weighted moving average with weights of 0.5, 0.3, and 0.2. Use the largest weight with the most recent data.

(b) Forecast the average annual food price index using exponential smoothing with α = 0.7 for all years from 2008 to 2014. Use the rate for 2008 as the starting forecast for 2008.

(c) Which of the methods in parts (a) and (b) produces better forecasts for the 3 years from 2011 to 2013? Answer on the basis of mean square error (MAD).

Problem 6

A company manufactures two products, Product A and Product B. The wholesale price and manufacturing cost of each product are shown below.

Item

Price

Cost

Assembly Times (hr)

A

$30

$10

2

B

$45

$15

4

The company will produce a minimum of 5,000 of each item. Given the number of hours, the company can sell no more than 8,000 of Item A and 10,000 of Item B. Suppose the company has 50,000 hours of assembly time available. How many of each item should it produce in order to maximize profits while meeting all necessary constraints? Give the LP model and use the graphical method to find the optimal solution.

Problem 7

A commercial real estate company is evaluating a proposed warehouse. The proposed site is near a rail terminal, but the state government may extend the highway to the area. In addition, the federal government is considering rebuilding the local port facilities. Below is the payoff table in monthly profit depending upon what government actions are taken. Based on the following criteria, what are the correct choices for terminal rental?

(a) Optimistic or maximax criterion

(b) Pessimistic or maximin criterion

(c) Equally likely or principle of insufficient reason criterion

Warehouse size (ft2)

Development projects

Rail terminal only

Highway expansion

Port rehabilitation

All

15000

10

25

35

40

30000

15

25

40

50

60000

20

30

45

75

100000

15

20

40

90

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