Question

he figures below show the weekly demand at an electrical repair workshop for a certain type of connector over a ten-week period : Week no. 1 2 3 4 5 6 10 7 8 9 26 21 21 26 No. demanded 26 23 24 24 26 26 Use exponential smoothing with a-value of 0.2 to smooth the data and obtain a forecast for week 11. The forecast for the 11th week is?. (Round your intermediate and final answers to two decimal places.)

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Answer to a math question he figures below show the weekly demand at an electrical repair workshop for a certain type of connector over a ten-week period : Week no. 1 2 3 4 5 6 10 7 8 9 26 21 21 26 No. demanded 26 23 24 24 26 26 Use exponential smoothing with a-value of 0.2 to smooth the data and obtain a forecast for week 11. The forecast for the 11th week is?. (Round your intermediate and final answers to two decimal places.)

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Hank

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97 Answers

### Solution:

Given:
-

\alpha = 0.2

S_1 = 26

### Calculations for Weeks 2 to 10:

#### Week 2:

S_2 = 0.2 \cdot 23 + 0.8 \cdot 26 = 25.4

#### Week 3:

S_3 = 0.2 \cdot 24 + 0.8 \cdot 25.4 = 25.12

#### Week 4:

S_4 = 0.2 \cdot 24 + 0.8 \cdot 25.12 = 24.90

#### Week 5:

S_5 = 0.2 \cdot 23 + 0.8 \cdot 24.90 = 25.12

#### Week 6:

S_6 = 0.2 \cdot 22 + 0.8 \cdot 25.12 = 25.30

#### Week 7:

S_7 = 0.2 \cdot 23 + 0.8 \cdot 25.30 = 25.44

#### Week 8:

S_8 = 0.2 \cdot 22 + 0.8 \cdot 25.44 = 24.55

#### Week 9:

S_9 = 0.2 \cdot 20 + 0.8 \cdot 24.55 = 23.84

#### Week 10:

S_{10} = 0.2 \cdot 20 + 0.8 \cdot 23.84 = 24.27

### Answer:
The forecasted demand for Week 11 using exponential smoothing with alpha = 0.2 is approximately

\boxed{24.27}

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