Final answer:
Using the multiplicative seasonal model, the projected demand for George’s sailboats in spring of year 5 is approximately 6,890 sailboats when the forecasted annual demand is given as 5,600 sailboats.
Step-by-step explanation:
To project the demand for George's sailboats in the spring of year 5 using a multiplicative seasonal model, we must first calculate the seasonal index for each season and then adjust the forecasted annual demand accordingly.
Steps to Calculate Seasonal Index:
- Find the average demand for each season over the past years.
- Calculate the average demand per season divided by the overall average demand across all seasons and years to get the seasonal index.
- Use the forecasted annual demand and multiply it by the seasonal index for spring to estimate spring's demand for year 5.
Let's illustrate with the provided data:
- Total demand over four years = (1,400+1,200+1,000+900) + (1,500+1,400+1,600+1,500) + (1,000+2,100+2,000+1,900) + (600+750+650+500) = 19,500.
- Total number of seasons = 4 years * 4 seasons/year = 16.
- Average demand per season = 19,500 / 16 = 1,218.75.
- Spring demand over four years = 1,500+1,400+1,600+1,500 = 6,000.
- Average spring demand = 6,000 / 4 = 1,500.
- Seasonal index for spring = Average spring demand / Average demand per season = 1,500 / 1,218.75 ≈ 1.2305.
- Forecasted annual demand for year 5 = 5,600.
- Projected spring demand for year 5 = Forecasted annual demand * Seasonal index for spring = 5,600 * 1.2305 ≈ 6,890 sailboats.
Therefore, the predicted demand level for George’s sailboats in the spring of year 5, according to the multiplicative seasonal model, will be approximately 6,890 sailboats.