Question

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 1 comma 480 1 comma 280 1 comma 040 900 Spring 1 comma 500 1 comma 400 1 comma 620 1 comma 500 Summer 1 comma 020 2 comma 120 2 comma 000 2 comma 000 Fall 640 810 670 560 George has forecasted that annual demand for his sailboats in year 5 will equal 6 comma 000 sailboats. Based on the given data and using the multiplicative seasonal​ model, the demand level for​ George's sailboats in the spring of year 5 will be nothing sailboats ​(enter a whole ​number).

Answer 1

To forecast the spring demand for sailboats in year 5 using the multiplicative seasonal model, calculate the average demand for previous springs, determine the seasonal index for spring, and then apply this index to the forecasted annual demand for year 5.

Step-by-step explanation:

To calculate the spring demand for George's sailboats in year 5 using a multiplicative seasonal model, we first need to determine the seasonal index for the spring season. We do this by averaging the past demand for spring, then dividing each spring's demand by this average to find the seasonal index. After that, we forecast the total demand for year 5 and distribute it among the seasons using their respective seasonal indices.

First, calculate the average spring demand:

• Year 1 Spring: 1,500 sailboats
• Year 2 Spring: 1,400 sailboats
• Year 3 Spring: 1,620 sailboats
• Year 4 Spring: 1,500 sailboats

Average Spring Demand = (1,500 + 1,400 + 1,620 + 1,500) / 4 = 1,505 sailboats

Then, calculate the seasonal indices for spring:

• Year 1 Spring Index: 1,500 / 1,505
• Year 2 Spring Index: 1,400 / 1,505
• Year 3 Spring Index: 1,620 / 1,505
• Year 4 Spring Index: 1,500 / 1,505

Average Spring Seasonal Index = (1,500/1,505 + 1,400/1,505 + 1,620/1,505 + 1,500/1,505) / 4

Now, George has forecasted an annual demand of 6,000 sailboats for year 5. The demand level for spring will be:

Spring Demand for Year 5 = Forecasted Annual Demand * Average Spring Seasonal Index

After calculating the Average Spring Seasonal Index, you multiply this by the forecasted annual demand to get the spring demand for year 5.

Answer 2

Answer: Spring forecast = 1759.5

Step-by-step explanation:

Unadjusted forecast =
`(6000)/(4)` = 1500

(1) For winter season:

Average =
`(Year1+year2+year3+year4)/(4)`

=
`(1480+1280+1040+900)/(4)`

= 1175

Seasonal Index =
`(Average\ of\ winter)/(Average\ of\ all\ season)`

=
`(1175)/(1283)`

= 0.915

Adjusted Forecast = Unadjusted forecast x Seasonal Index

= 1500 × 0.915

= 1372.5

(2) For spring season:

Average =
`(Year1+year2+year3+year4)/(4)`

=
`(1500+1400+1620+1500)/(4)`

= 1505

Seasonal Index =
`(Average\ of\ winter)/(Average\ of\ all\ season)`

=
`(1505)/(1283)`

= 1.173

Adjusted Forecast = Unadjusted forecast x Seasonal Index

= 1500 × 1.173

= 1759.5

(3) For summer season:

Average =
`(Year1+year2+year3+year4)/(4)`

=
`(1020+2120+2000+2000)/(4)`

= 1785

Seasonal Index =
`(Average\ of\ winter)/(Average\ of\ all\ season)`

=
`(1785)/(1283)`

= 1.39

Adjusted Forecast = Unadjusted forecast x Seasonal Index

= 1500 × 1.39

= 2086.9

(4) For fall season:

Average =
`(Year1+year2+year3+year4)/(4)`

=
`(640+810+670+560)/(4)`

= 670

Seasonal Index =
`(Average\ of\ winter)/(Average\ of\ all\ season)`

=
`(670)/(1283)`

= 0.522

Adjusted Forecast = Unadjusted forecast x Seasonal Index

= 1500 × 0.522

= 783.32

∴ Spring forecast = 1759.5