To address your request, I'll compute the forecasts using a six-period simple moving average (SMA) model. The forecast for each period will be the average demand of the preceding six periods. The Mean Absolute Deviation (MAD) will also be calculated, and finally, the forecast and associated error for the 11th period will be determined.

Step 1: Compute the forecasts using a six-period simple moving average

To calculate the forecast for a period, we'll use the average of the previous six periods' demand. Since we can't forecast for the first six periods, the first forecast will be for period 7.

Formula: $\text{SMA}_n = \frac{D_{n-1} + D_{n-2} + D_{n-3} + D_{n-4} + D_{n-5} + D_{n-6}}{6}$

Forecasts:

• Forecast for period 7 = $\frac{130 + 122 + 121 + 112 + 141 + 105}{6}$
• Forecast for period 8 = $\frac{122 + 121 + 112 + 141 + 105 + 116}{6}$
• Forecast for period 9 = $\frac{121 + 112 + 141 + 105 + 116 + 120}{6}$
• Forecast for period 10 = $\frac{112 + 141 + 105 + 116 + 120 + 142}{6}$

Let's compute these values first, and then move forward.Here are the forecasts for periods 7 through 10 using a six-period simple moving average model:

• Forecast for period 7: 121.8
• Forecast for period 8: 119.5
• Forecast for period 9: 119.2
• Forecast for period 10: 122.7

Step 2: Compute the Mean Absolute Deviation (MAD)

The MAD is calculated as the average of the absolute forecast errors (the absolute difference between the actual demand and forecasted demand).

The formula for MAD is: $\text{MAD} = \frac{\sum |D_i - F_i|}{n}$ Where $D_i$ is the actual demand and $F_i$ is the forecast.

Let's now compute the MAD using the forecasts and actual demand for periods 7 through 10.The Mean Absolute Deviation (MAD) for the forecasts from periods 7 to 10 is 7.8.

Step 3: Forecast demand for period 11

To forecast the demand for period 11, we'll use the six-period simple moving average of the actual demands from periods 5 to 10.

$\text{Forecast for period 11} = \frac{141 + 105 + 116 + 120 + 142 + 125}{6}$

Let me compute that forecast.The forecast demand for period 11, using the six-period simple moving average model, is 124.8.

Step 4: Compute the error associated with the 11th-period forecast

Since the actual demand for period 11 is not provided, the error cannot be computed at this time. However, the error would be calculated using the formula:

$\text{Error for period 11} = D_{11} - F_{11}$ Where $D_{11}$ is the actual demand for period 11 (once available), and $F_{11} = 124.8$.

Would you like further clarification or more details? Here are some related questions you could explore:

1. How would the forecast change if we used a different period for the moving average?
2. What happens to MAD when there are outliers in the data?
3. How does the simple moving average model compare to weighted moving averages?
4. Can we apply exponential smoothing to forecast demand?
5. What strategies can be used to reduce forecast errors?

Tip: The simple moving average model works best when demand is relatively stable and there are no strong trends or seasonal patterns.