Chapter 5
1. The forecasting staff for the Prizer Corporation has developed a model to predict sales of its air-cushioned-ride snowmobiles. The model specifies that sales S vary jointly with disposable personal income Y and the population between ages 15 and 40, Z, and inversely with the price of the snowmoblies P. Based on past data, the best estimate of this relationship is *YZ/P where k has been estimated (with past data) to equal 100.
a. If Y = $11,000, Z = $1,200, and P = $20,000, what value would you predict for S ?
b. What happens if P is reduced to $17,500?
c. How would you go about developing a value for k?
d. What are the potential weaknesses of his model?
5. A firm experienced the demand shown in the following table.
year ------ actual demand---- 5 yr moving avg --- 3 yr moving avg-- exponential smoothing -- exponential smoothing ( ) --- ( ) _________________________________________________________________________________________________ 2000 | 800 | xxxx | xxxx | xxxx | xxxxx 2001 | 925 | xxxx | xxxx | _____ | __________ 2002 | 900 | xxxx | xxxx | ______ | __________ 2003 | 1025 | xxxx | _____ | ________ | ___________ 2004 | 1150 | xxxx | ______ | _________ | ____________ 2005 | 1160 | _____ | _______ | __________ | _____________ 2006 | 1200 | _______ | _______ | __________ | ____________ 2007 | 1150 | _______ | ________ | ___________ | ____________ 2008 | 1270 | ________ | ________ | ___________ | ____________ 2009 | 1290 | _________ | ________ | ____________ | ___________ 2010 | * | _________ | _________ | ____________ | ____________ Unknown future value to be forecast.
a. Fill in the table by preparing forecasts based on a five- year moving average, a three- year moving average, and exponential smoothing( with a and a ). Note: The exponential smoothing forecasts may be begun by assuming Yt+
b. Using the forecasts from 2005 through 2009, compare the accuracy of each of the forecasting methods based on the RMSE criterion.
c. Which forecast would you have used for 2010? Why?
6. The economic analysis division of Mapco Enterprises has estimated the demand function for its line of weed trimmers as ,000 + 0.4N - 350Pm + 90Ps where of new homes completed in the primary market area of the Mapco trimmer of its competitor's Surefire trimmer In 2010, 15,000 new homes are expected to be completed in the primary market area. Mapco plans to charge $50 for its trimmer. The Surefire trimmer is expected to sell for $55.
a. What sales are forecast for 2010 under these conditions?
b. If its competitor cuts the price of the Surefire trimmer to $50, what effect will this have on Mapco's sales?
c. What effect would a 30 percent reduction in the number of new homes completed have on Mapco's sales ( ignore the impact of the price cut of the Surefire trimmer)?
9. Savings-Mart (a chain of discount department stores) sells patio and lawn furniture. Sales are seasonal, with higher sales during the spring and summer quarters and lower sales during the fall and winter quarters. The company developed the following quarterly sales forecasting model:
+ 0.125t 2.75D1t + 2.25D2t + 3.50D3t
Where sales ($ million) in quarter t
sales ($ million) when
period (quarter) where the fourth quarter of First quarter of , second quarter of ,. . .
for first-quarter observations 0 otherwise
for second quarter observations 0 otherwise
for third-quarter observations 0 otherwise
Forecast Savings-Mart s sales of patio and lawn furniture for each quarter of 2010.
