4.27 A manufacturer of sailboats had actual demand for his boats during each of
ID: 409123 • Letter: 4
Question
4.27 A manufacturer of sailboats had actual demand for his boats during each of the past four seasons is as follows:
SEASON 1 2 3 4
WINTER 1,400 1,200 1,000 900
SPRING 1,500 1,400 1,600 1,500
SUMMER 1,000 2,100 2,000 1,900
FALL 600 750 650 500
The owner has forecasted that the annual demand for his boats in year 5 will equal 5,000 sailboats. Based on this data and the multiplicative seasonal model, what will be the demand level for his boats in the spring of year 5?
Explanation / Answer
Season
year
Average
1-4
Demand
Average seasonal demand
Seasonal index
1
2
3
4
Winter
1400
1200
1000
900
1125
1250
0.9
Spring
1500
1400
1600
1500
1500
1250
1.2
Summer
1000
2100
2000
1900
1750
1250
1.4
Fall
600
750
650
500
625
1250
0.5
Total
Average Seasonally demand = 5000/4 = 1250
5000
Seasonal index = (Average 1-4 demand) / (Average seasonal demand )
Forecasted value for the spring of year 5 is = 5000 / 4 * (1.2) = 1500
Season
year
Average
1-4
Demand
Average seasonal demand
Seasonal index
1
2
3
4
Winter
1400
1200
1000
900
1125
1250
0.9
Spring
1500
1400
1600
1500
1500
1250
1.2
Summer
1000
2100
2000
1900
1750
1250
1.4
Fall
600
750
650
500
625
1250
0.5
Total
Average Seasonally demand = 5000/4 = 1250
5000
Seasonal index = (Average 1-4 demand) / (Average seasonal demand )
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