MATHEMATICS

4.1 The following gives the number of pints of type B blood used at Woodlawn Hospital in the past 6 weeks:

a) Forecast the demand for the week of October 12 using a 3-week moving average.b) Use a 3-week weighted moving average, with weights of .1, .3, and .6, using .6 for the most recent week. Forecast demand for the week of October 12.c) Compute the forecast for the week of October 12 using exponential smoothing with a forecast for August 31 of 360 and a 5 .2. PX

4.3 Refer to Problem 4.2. Develop a forecast for years 2 through 12 using exponential smoothing with a 5 .4 and a fore-cast for year 1 of 6. Plot your new forecast on a graph with the actual data and the naive forecast. Based on a visual inspection, which forecast is better?

Answers for 4.2:

(a) None obvious.

(b) 7, 7.67, 9, 10, 11, 11, 11.33, 11, 9

(c) 6.4, 7.8, 11, 9.6, 10.9, 12.2, 10.5, 10.6, 8.4

(d) The 3-yr. moving average.

4.5 The Carbondale Hospital is considering the purchase of a new ambulance. The decision will rest partly on the anticipated mileage to be driven next year. The miles driven during the past 5 years are as follows:

a) Forecast the mileage for next year (6th year) using a 2-year moving average.b) Find the MAD based on the 2-year moving average. (Hint: You will have only 3 years of matched data.)c) Use a weighted 2-year moving average with weights of .4 and .6 to forecast next year’s mileage. (The weight of .6 is for the most recent year.) What MAD results from using this approach to forecasting? (Hint: You will have only 3 years of matched data.)d) Compute the forecast for year 6 using exponential smoothing, an initial forecast for year 1 of 3,000 miles, and a 5 .5. PX

4.25 The following gives the number of accidents that occurred on Florida State Highway 101 during the past 4 months:

Forecast the number of accidents that will occur in May, using least-squares regression to derive a trend equation.PX

4.27 George Kyparisis owns a company that manufactures sailboats. Actual demand for George’s sailboats during each of the past four seasons was as follows:

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