32. The Grand Bakery produces special sourdough rolls every day. Any rolls that are not sold each day are given to the employees. They have collected the sales data below from the past week:

Day

Rolls sold

1

50

2

50

3

48

4

60

5

53

6

?

What is the forecast for Day 6 if they use a 3-day weighted moving average with weights of 0.6 (latest), 0.3, and 0.1?

Question

32. The Grand Bakery produces special sourdough rolls every day. Any rolls that are not sold each day are given to the employees. They have collected the sales data below from the past week:

Day

Rolls sold

1

50

2

50

3

48

4

60

5

53

6

?

What is the forecast for Day 6 if they use a 3-day weighted moving average with weights of 0.6 (latest), 0.3, and 0.1?

BlackTom AI · Accepted Answer

A 3-day weighted moving average uses the three most recent actuals with weights 0.6 (most recent), 0.3 (second most recent), and 0.1 (third most recent).

1. Relevant knowledge points and concepts
- Moving average forecasting smooths past observations to predict the next period.
- A weighted moving average multiplies each of the most recent observations by assigned weights that sum to 1, giving more influence to more recent data.
- For Day 6, use Day 5 (latest), Day 4 (second), and Day 3 (third) with weights 0.6, 0.3, 0.1 respectively.

2. Complete reasoning process step by step
- Identify the three most recent actual sales before Day 6: Day 5 = 53, Day 4 = 60, Day 3 = 48.
- Multiply each by its weight and sum the products to get the forecast for Day 6.

3. Calculations with intermediate steps
- Weight × value for Day 5 (most recent): 0.6 × 53 = 31.8
- Weight × value for Day 4: 0.3 × 60 = 18.0
- Weight × value for Day 3: 0.1 × 48 = 4.8
- Sum: 31.8 + 18.0 + 4.8 = 54.6

4. Why the correct answer is correct
- The forecast 54.6 is the direct result of applying the specified weights to the correct three most recent days. The calculation respects the order of recency (0.6 to Day 5, 0.3 to Day 4, 0.1 to Day 3) and uses all weights that sum to 1, producing the weighted average.

5. Why the other options are incorrect
- 58.6: No combination of the given weights applied correctly to the three most recent days yields 58.6; this likely results from misordering or incorrect values.
- 52.8 and 53.7: These are also inconsistent with the correct weighted computation shown above; they would result from applying wrong weights, wrong days, or arithmetic errors.

6. Conclusion
- The computed 3-day weighted moving average forecast for Day 6 is 54.6, which matches the provided correct answer.

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