A coffee shop owner wants to estimate demand for the next two quarters for hot chocolate. Sales data consist of trend and seasonality. a. Quarter relatives are 1.20 for the first quarter, 1.10 for the second quarter, 0.75 for the third quarter, and 0.95 for the fourth quarter. Use this information

Question

A coffee shop owner wants to estimate demand for the next two quarters for hot chocolate. Sales data consist of trend and seasonality.

a. Quarter relatives are 1.20 for the first quarter, 1.10 for the second quarter, 0.75 for the third quarter , and 0.95 for the fourth quarter . Use this information to deseasonalize sales for quarters 1 through 8.

b. Using the appropriate values of quarter relatives and the equation [latex]F_t = 124 + 7.5t[/latex] for the trend component, estimate demand for periods 9 and 10.

Accepted Answer

a.

Period	Quarter	Sales (gal.)	[latex]\div[/latex]	Quarter Relative	=	Deseasonalized Sales
1	1	158.4	[latex]\div[/latex]	1.20	=	132·0
2	2	153·0	[latex]\div[/latex]	1.10	=	139.1
3	3	110·0	[latex]\div[/latex]	0.75	=	146.7
4	4	146.3	[latex]\div[/latex]	0.95	=	154·0
5	1	192·0	[latex]\div[/latex]	1.20	=	160·0
6	2	187·0	[latex]\div[/latex]	1.10	=	170·0
7	3	132·0	[latex]\div[/latex]	0.75	=	176·0
8	4	173.8	[latex]\div[/latex]	0.95	=	182.9

b. The trend values are :

Period 9: [latex]F_t + 124 + 7.5(9) = 191.5[/latex]

Period 10 : [latex]F_t + 124 + 7.5(10) = 199.0[/latex]

Period 9 is a first quarter and period 10 is a second quarter. Multiplying each trend value by the appropriate quarter results in:

Period 9: [latex] 191.5(1.20) = 229.8[/latex]

Period 10: [latex] 199.0(1.10) = 218.9[/latex]

Question 3.7: A coffee shop owner wants to estimate demand for the next tw...

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