mathematics

12. For the demand data in Problem 11, develop a seasonally adjusted forecast for year 4. (Use a linear trend line model to develop a forecast estimate for year 4.) Which forecast model do you perceive to be more accurate: the exponential smoothing model from Problem 11 or the seasonally adjusted forecast?
13. Develop a seasonally adjusted forecast for the demand data for fertilizer found in Problem 3. Then use a linear trend line model to compute a forecast estimate for demand in year 4.
14. Monaghan’s Pizza delivery service has randomly selected 8 weekdays during the past month and recorded orders for pizza at four different time periods per day: Day
Time Period 1 2 3 4 5 6 7 8 10:00 A . M .–3:00 P . M . 62 49 53 35 43 48 56 43 3:00 P . M .–7:00 P . M . 73 55 81 77 60 66 85 70 7:00 P . M .–11:00 P . M . 42 38 45 50 29 37 35 44 11:00 P . M .–12:00 A . M . 35 40 36 39 26 25 36 31 Develop a seasonally adjusted forecasting model for daily pizza demand and forecast demand for each of the time periods for a single upcoming day. 15. The Cat Creek Mining Company mines and ships coal. It has experienced the following demand for coal during the past 8 years: Year Coal Sales (tons) 1 4,260 2 4,510 3 4,050 4 3,720 5 3,900 6 3,470 7 2,890 8 3,100
Develop an adjusted exponential smoothing model ( a = .30, b = .20) and a linear trend line model and compare the forecast accuracy of the two by using MAD. Indicate which forecast seems to be more accurate.
16. The River is a literary magazine published by the English Department at Tech. It has a 70-year history and enjoys an excellent reputation for providing a literary outlet for aspiring Ap- palachian writers in particular. However, its sales, mostly through independent bookstores and college libraries, have never been very large. Several years ago, the magazine’s advisory board decided to create a Web site and post the bi-monthly issues online for free access. Due to poor economic conditions and state budget cuts, Tech recently withdrew funding for the magazine, and in order to make up for this financial loss, the magazine’s staff has decided to try to sell ad- vertising (especially to local and regional businesses) on the magazine’s Web site. In order to 730 CHAPTER 15 FORECASTING sell advertising, the magazine’s staff would like to be able to provide potential advertisers with a forecast of the number of “visits” the Web site might receive in future months. Following is the number of monthly visits the Web site has received for the 24 months that it has existed:
Month Web Site Visits Month Web Site Visits 1 537 13 822 2 375 14 677 3 419 15 1,031 4 276 16 657 5 445 17 983 6 512 18 774 7 670 19 1,210 8 561 20 811 9 705 21 1,137 10 619 22 763 11 768 23 1,225 12 645 24 941
Develop a linear trend line forecast, an exponential smoothing forecast ( a = 0.60), and a 3-month weighted moving average (with the most recent month weighted by 0.50, the next closest month by 0.30, and the final month by 0.20). Indicate which one you believe is the most accurate forecast model and the forecast for month 25.
17. The Beaver Creek Pottery Company sells bowls and mugs, hand-made by Native American arti- sans, at a craft store and through a Web site. Making these items requires a special type of clay and a large amount of individual person-hours, so for planning purposes, the company would like to forecast future demand, specifically through its Web site, which has increasingly become the primary source of sales. Following is the company’s Web site demand (in items sold) for the past 36 months:
Month Sales Month Sales Month Sales 1 345 13 415 25 344 2 411 14 395 26 286 3 266 15 298 27 455 4 347 16 377 28 634 5 506 17 418 29 502 6 278 18 522 30 388 7 411 19 421 31 427 8 510 20 384 32 561 9 198 21 455 33 447 10 387 22 506 34 395 11 344 23 478 35 414 12 412 24 613 36 522
Develop a linear trend forecast model, an exponentially smoothed model ( a = 0.20), and a 5-month moving average forecast model and indicate which one you think should be used to forecast Web site demand. PROBLEMS 731

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