To forecast demand using exponential smoothing, we can apply the formula:

$F_t = \alpha \cdot D_{t-1} + (1 - \alpha) \cdot F_{t-1}$

Where:

• $F_t$ is the forecast for time period $t$,
• $D_{t-1}$ is the actual demand for the previous time period,
• $F_{t-1}$ is the forecast for the previous time period, and
• $\alpha$ is the smoothing constant, given as 0.3.

We'll start with the actual shipment data from September, and the forecast will begin from October onwards. Assuming the initial forecast for September is equal to the actual September value (6.7), we can proceed with forecasting for each subsequent month.

Let's calculate the forecasts step by step. I'll generate the forecasts for the months October to August using the exponential smoothing method.Here is the forecast for demand using exponential smoothing with a constant of $\alpha = 0.3$ from October to August:

Month	Actual Shipments	Forecast
Oct	5.6	6.70
Nov	6.0	6.37
Dec	8.0	6.26
Jan	5.5	6.78
Feb	5.1	6.40
Mar	6.9	6.01
Apr	5.5	6.28
May	5.5	6.04
Jun	7.6	5.88
Jul	5.9	6.40
Aug	6.0	6.25

Would you like more details on how the smoothing was calculated, or do you have any questions?

Further exploration:

1. How would a different smoothing constant affect the forecast?
2. How can we compare the accuracy of the forecast using this method?
3. Can you calculate the error between the actual and forecasted values?
4. How would the forecast change if the initial forecast was different?
5. What other forecasting methods could be used to predict demand?

Tip: Exponential smoothing gives more weight to recent observations, which is why adjusting the smoothing constant can dramatically change the results.