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7. Marie Bain is the production manager at a company that manufactures hot water heaters. Marie needs a demand forecast for the next few years to help decide whether to add new production capacity. The company's sales history (in thousands of units) is shown in the table below. Use exponential smoothing with trend adjustment to forecast demand for period 6. The initial forecast for period 2 was 20 units; the initial estimate of trend was 2.00. The smoothing constants are = .2 and = .4 (5 points)

Period Actual Forecast Trend FIT

1 22 20 2.00 22

2 26 18.8 18.8 37.6

3 25 5.2 5.2 10.4

4 28 5 5 10

5 27 5.6 5.6 11.2

6 29 5.4 5.4 10.8

Period 2.2 * 22 + (1 - 0.2) (20 + 2) = 18.8

0.4 * (18.8 - 20) + (1 - 0.4) * 2 = 18.8

18.8 + 18.8 = 37.6

Period 30.2 * 26 + (1 - 0.2) (18.8 + 18.8) = 5.2

0.4 * (5.2 - 18.8) + (1 - 0.4) * 18.8 = 5.2

5.2 + 5.2 = 10.4

Period 40.2 * 25 + (1 - 0.2) (5.2 + 5.2) = 5

0.4 * (5 - 5.2) + (1 - 0.4) * 5.2 = 5

5 + 5 = 10

Period 50.2 * 28 + (1 - 0.2) (5 + 5) = 5.6

0.4 * (5.6 - 5) + (1 - 0.4) * 5 = 5.6

5.6 + 5.6 = 11.2

Period 60.2 * 27 + (1 - 0.2) (5.6 + 5.6) = 5.4

0.4 * (5.4 - 5.6) + (1 - 0.4) * 5.6 = 5.4

5.4 + 5.4 = 10.8

Period 70.2 * 29 + (1 - 0.2) (5.4 + 5.4) = 5.8

0.4 * (5.8 - 5.4) + (1 - 0.4) * 5.4 = 5.8

5.8 + 5.8 = 11.6