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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).

Respuesta :

Answer: Spring forecast = 1759.5

Explanation:

Unadjusted forecast = [tex]\frac{6000}{4}[/tex] = 1500

(1) For winter season:

Average = [tex]\frac{Year1+year2+year3+year4}{4}[/tex]

= [tex]\frac{1480+1280+1040+900}{4}[/tex]

= 1175

Seasonal Index = [tex]\frac{Average\ of\ winter}{Average\ of\ all\ season}[/tex]

=[tex]\frac{1175}{1283}[/tex]

= 0.915

Adjusted Forecast = Unadjusted forecast x Seasonal Index

= 1500 × 0.915

= 1372.5

(2) For spring season:

Average = [tex]\frac{Year1+year2+year3+year4}{4}[/tex]

= [tex]\frac{1500+1400+1620+1500}{4}[/tex]

= 1505

Seasonal Index = [tex]\frac{Average\ of\ winter}{Average\ of\ all\ season}[/tex]

=[tex]\frac{1505}{1283}[/tex]

= 1.173

Adjusted Forecast = Unadjusted forecast x Seasonal Index

= 1500 × 1.173

= 1759.5

(3) For summer season:

Average = [tex]\frac{Year1+year2+year3+year4}{4}[/tex]

= [tex]\frac{1020+2120+2000+2000}{4}[/tex]

= 1785

Seasonal Index = [tex]\frac{Average\ of\ winter}{Average\ of\ all\ season}[/tex]

=[tex]\frac{1785}{1283}[/tex]

= 1.39

Adjusted Forecast = Unadjusted forecast x Seasonal Index

= 1500 × 1.39

= 2086.9

(4) For fall season:

Average = [tex]\frac{Year1+year2+year3+year4}{4}[/tex]

= [tex]\frac{640+810+670+560}{4}[/tex]

= 670

Seasonal Index = [tex]\frac{Average\ of\ winter}{Average\ of\ all\ season}[/tex]

=[tex]\frac{670}{1283}[/tex]

= 0.522

Adjusted Forecast = Unadjusted forecast x Seasonal Index

= 1500 × 0.522

= 783.32

∴ Spring forecast = 1759.5