Question

A large Portland manufacturer wants to forecast demand for a piece of​ pollution-control equipment. A review of past sales

​(Upper A Subscript tAt​),

as shown​ below, indicates that an increasing trend is present.  Smoothing constants are assigned the values of alphaα = 0.20 and betaβ = 0.4

The firm assumes the initial forecast for month 1 ​(Upper F 1F1​) was 11.00 units and the trend over that period Upper T 1T1 was 2.00 units.

Using​ trend-adjusted exponential​ smoothing, Forecasts (Upper F Subscript tFt​), Trend ​(Upper T Subscript tTt​), and Forecasts Including Trend ​(FIT Subscript tFITt​) for months 1 through 4 have already been developed and are provided below. Continue with the process and determine Upper F Subscript tFt​, Upper T Subscript tTt​, and FIT Subscript tFITt for months 5 and 6 ​(round your responses to two decimal​ places):

                                                                                                                                      

Month ​(t​)	Actual Demand ​(Upper A Subscript tAt​)	Forecast ​(Upper F Subscript tFt​)	Trend ​(Upper T Subscript tTt​)	Forecast Including Trend ​(FIT Subscript tFITt​)
1	12.012.0	11.0011.00	2.002.00	13.0013.00
2	17.017.0	12.8012.80	1.921.92	14.7214.72
3	24.024.0	15.1815.18	2.102.10	17.2817.28
4	19.019.0	18.6218.62	2.642.64	21.2621.26
5	22.022.0	?	?	?
6	23.023.0	?	?	?
7	31.031.0	?	?	?
8	26.026.0	?	?	?
9	35.035.0	?	?	?
10	?	?	?	?

Find ''?''

Answer 1

Alpha	0.2
Beta	0.4
t	At	Ft	Tt	F/Tt
4	19	18.62	2.64	21.26
5	22	20.808	2.4592	23.2672
6	23	23.01376	2.357824	25.37158
7	31	24.89727	2.168097	27.06536
8	26	27.85229	2.482868	30.33516
9	35	29.46813	2.136055	31.60418
10	?	32.28335	2.407721	34.69107