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 the S vary jointly with disposable personal income Y and the population between ages 15 and 40,Z, and inversely with the price of the snowmobiles P. Based on the past data, the best estimate of this relationship is S= K *YZ/P where k has been estimated (with the pst data) to equal 100. If Y=$11,000, Z= $1,200, and P=$20,000

a) what value would you predict for S?

Answer:

The given function is S=K*YZ/P at the given values of; k=100 Y=$11,000 Z=$1,200 P=$20,000 the value of S is: S=100(11000*1200)/20000= $66,000 so there would be a sales of $66,000 at above given values.

5. A firm experienced the demand shown in the following table.

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 w = 0.9 and a w = 0.3). The exponential smoothing forecasts may be begun by assuming Ŷt+1 = 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?

5- year 3-YearExponentialExponential

Actual Moving MovingSmoothingSmoothing

YearDemandAverageAcverage(W= 0.9 )(W= 0.3 )

2000800xxxxxxxxxxxxXxxx

2001925xxxxxxxx687.5762.5

2002900xxxxXxxx947.5932.5

20031025xxxx875787.5862.5

20041150xxxx950912.5987.5

20051160960102511411147

200612001032111211241148

200711501087117012451215

200812701137117010421114

200912901186120712521264

2010*12141237

Sum91399433

RMSE= 9139/9

=1,015 when W=0.9

RMSE=9433/9

=1,048 When W=0.3

I would choose to use W=9 because it has the least amount of change between the two numbers. We should always use the number with least amount of deviation.

6. The economic analysis division of Mapco Enterprises has estimated the demand function for its line of weed trimmers as Qd = 18,000 + 0.4N - 350Pm + 90Ps

where N = number of new homes completed in the primary market area Pm = price of the Mapco trimmer Ps = price 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)?

Answer:

Qd-2006= 18,000+6000-17,500+4950=11450. Ps=$50,Qd= 18,000+6000-17500+4500=11,000. 15,000-15000x0.30=10,500 Qd=18,000+4200-17500+4950=9,650. 350 means dQd/dPm, or if Pm increases 1 unit,Qd will decline 350 units. 90 means if Ps increases 1 unit,Qd will increase 90 unit. Mapco and Surefire services are substitutes.

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: Yt= 8.25 + 0.125t 2.75D1t + 0.25D2t + 3.50D3t Where Yt = predicted sales ($ million) in quarter t 8.25 = quarterly sales ($ million) when t = 0 t = time period (quarter) where the fourth quarter of 2002 = 0 First quarter of 2003 = 1, second quarter of 2003 = 2D1t = 1 for first-quarter observations 0 otherwise D2t = 1 for second quarter observations 0 otherwise D3t = 1 for third-quarter observations 0 otherwise a). Forecast Savings-Mart's sales of patio and lawn furniture for each quarter of 2010.

1st quarter

y=...