Math Problem Statement

Sales of tablet computers at Marika​ Gonzalez's electronics store in​ Washington, D.C., over the past 10 weeks are shown in the table​ below:                                                                                                                    
Week 1 2 3 4 5 6 7 8 9 10 Demand 21 20 28 37 24 29 37 20 25 28

Part 2 ​a) The forecast for weeks 2 through 10 using exponential smoothing with alpha ​= 0.60 and a week 1 initial forecast of 21.0 are ​(round your responses to two decimal​ places):

Solution

The forecast for weeks 2 through 10 using exponential smoothing with α=0.60\alpha = 0.60 and an initial forecast of 21.0 is as follows:

  • Week 2: 21.00
  • Week 3: 20.40
  • Week 4: 24.96
  • Week 5: 32.18
  • Week 6: 27.27
  • Week 7: 28.31
  • Week 8: 33.52
  • Week 9: 25.41
  • Week 10: 25.16

Would you like more details or explanations on any part of the calculation?

Here are 5 related questions to expand the discussion:

  1. How does the value of α\alpha affect the forecasts in exponential smoothing?
  2. What would the forecasts look like if α\alpha were set to 0.30?
  3. How does exponential smoothing compare to moving averages for forecasting?
  4. Can you derive the Mean Squared Error (MSE) of these forecasts?
  5. How can you adjust forecasts if there is a sudden trend change in demand?

Tip: A higher α\alpha value gives more weight to recent demand, making the forecast more responsive to recent changes.

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Math Problem Analysis

Mathematical Concepts

Exponential Smoothing
Forecasting
Time Series Analysis

Formulas

Exponential Smoothing Formula: F_t = α * D_{t-1} + (1 - α) * F_{t-1}

Theorems

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Suitable Grade Level

College/University Level (Statistics or Business)