Let's solve each part of this problem step-by-step.

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Part (a): Three-Month Moving Average Forecast for This Month

To find a forecast using a simple three-month moving average, we average the demand of the last three months.

1. Three months ago: 400 units
2. Two months ago: 350 units
3. Last month: 325 units

The moving average forecast for this month is calculated as:

$\text{Forecast for this month} = \frac{400 + 350 + 325}{3} = \frac{1075}{3} = 358.33 \text{ units}$

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Part (b): Forecast for Next Month with Actual Demand of 300 Units This Month

If the actual demand for this month turns out to be 300 units, we can use it to create a new three-month moving average for the forecast for next month.

1. Two months ago: 350 units
2. Last month: 325 units
3. This month (actual): 300 units

So, the three-month moving average forecast for next month would be:

$\text{Forecast for next month} = \frac{350 + 325 + 300}{3} = \frac{975}{3} = 325 \text{ units}$

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Part (c): Forecast for This Month Using Simple Exponential Smoothing

For exponential smoothing, the formula is:

$\text{Forecast}_{\text{this month}} = \alpha \times \text{Actual demand}_{\text{last month}} + (1 - \alpha) \times \text{Forecast}_{\text{last month}}$

Where:

• $\alpha = 0.20$ (smoothing constant),
• Actual demand last month = 325 units,
• Forecast three months ago = 450 units (given).

We will calculate the forecast for each month step-by-step until this month.

Step 1: Forecast Two Months Ago

$\text{Forecast}_{\text{two months ago}} = 0.20 \times 400 + 0.80 \times 450 = 80 + 360 = 440 \text{ units}$

Step 2: Forecast Last Month

$\text{Forecast}_{\text{last month}} = 0.20 \times 350 + 0.80 \times 440 = 70 + 352 = 422 \text{ units}$

Step 3: Forecast This Month

$\text{Forecast}_{\text{this month}} = 0.20 \times 325 + 0.80 \times 422 = 65 + 337.6 = 402.6 \text{ units}$

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Summary of Answers

1. Part (a): Forecast for this month using a three-month moving average = 358.33 units.
2. Part (b): Forecast for next month (if actual demand this month is 300) = 325 units.
3. Part (c): Forecast for this month using exponential smoothing = 402.6 units.

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Would you like a deeper explanation for any part of this solution?

Related Questions to Explore

1. How would the forecast change if the smoothing constant was 0.3 instead of 0.2?
2. What would be the effect of increasing the period in the moving average to four months?
3. How does exponential smoothing differ from weighted moving average forecasting?
4. What are the benefits of using a moving average forecast versus exponential smoothing?
5. Can we adjust the smoothing constant dynamically for more responsive forecasting?

Tip

Using a higher smoothing constant ($\alpha$) in exponential smoothing will make the forecast more responsive to recent demand changes but can lead to more variability.