Problem Set 3   
4.1, 4.3, 4.5, 4.27, 4.31., and 4.37   
    
4.1 The following gives the number of pints of type B blood used at Woodlawn Hospital in the past 6 weeks:    
    
 Week of Pints Used  
 8/31/2013 360  
 9/7/2013 389  
 9/14/2013 410  
 9/21/2013 381  
 9/28/2013 368  
 10/5/2013 374  
    
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 an a of .2.

4.3 Refer to Problem 4.2. Develop a forecast for years 2 through 12 using exponential smoothing with a = .4 and a forecast 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?    
 Year Demand Forecast Naïve Forecast
 1 7 6.0 7
 2 9 6.4 9
 3 5 7.4 5
 4 9 6.5 9
 5 13 7.5 13
 6 8 9.7 8
 7 12 9.0 12
 8 13 10.2 13
 9 9 11.3 9
While the Naïve forecast goes higher on the chart, the forecast that used exponential smoothing seems to be more consistent.    

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:  
 Year Mileage
 1 3,000
 2 4,000
 3 3,400
 4 3,800
 5 3,700
What MAD results from using this approach to forecasting? (Hint: You will have only 3 years of matched data.)
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.)

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:     YEAR   
 SEASON 1 2 3 4
 Winter 1400 1200 1000 900
 Spring 1500 1400 1600 1500
 Summer 1000 2100 2000 1900
 Fall 600 750 650 500
George has forecasted that annual demand for his sailboats in year 5 will equal 5,600 sailboats.Based on this data and the multiplicative seasonal model, what will the demand level be for George’s sailboats in the spring of year 5?  

4.31 Café Michigan’s manager, Gary Stark, suspects that demand for mocha latte coffees depends on the price being charged. Based on historical observations, Gary has gathered the following data, which show the numbers of these coffees sold over six different price values:  
 Price Number Sold
 $2.70 760
 $3.50 510
 $2.00 980
 $4.20 250
 $3.10 320
 $4.05 480
Using these data, how many mocha latte coffees would be forecast to be sold according to simple linear regression if the price per cup were $2.80?  
   
4.37 Sales of tablet computers at Ted Glickman’s electronics store in Washington, D.C., over the past 10 weeks are shown in the table below:    
 Week Demand Week  Demand 
 1 20 6 29 
 2 21 7 36 
 3 28 8 22 
 4 37 9 25 
 5 25 10 28