To determine the seasonalized forecast for February 2016, we first need to calculate the sales forecast without seasonality using the given model:
\[ \text{Sales} = 6 * t + 327.00 \]
Next, we need to identify the value of \( t \) for February 2016. Since \( t \) starts from January 2015, we can calculate \( t \) as follows:
- January 2015 corresponds to \( t = 0 \)
- February 2015 corresponds to \( t = 1 \)
- March 2015 corresponds to \( t = 2 \)
- ...
- December 2015 corresponds to \( t = 11 \)
- January 2016 corresponds to \( t = 12 \)
- February 2016 corresponds to \( t = 13 \)
So for February 2016, \( t = 13 \).
Now we can substitute \( t = 13 \) into the sales forecast equation:
\[ \text{Sales} = 6 * 13 + 327.00 \]
Calculating it step-by-step:
\[ = 78 + 327 = 405 \]
The forecasted sales without seasonality for February 2016 is \( 405 \).
Next, we apply the seasonal factor for February. From the table, the seasonal factor for February is \( 0.8752 \).
Now, to get the seasonalized forecast for February 2016, we multiply the non-seasonal forecast by the seasonal factor:
\[ \text{Seasonalized Sales} = \text{Sales without seasonality} * \text{Seasonal Factor} \] \[ \text{Seasonalized Sales} = 405 * 0.8752 \]
Calculating this:
\[ = 405 * 0.8752 \approx 354.606 \]
Rounding to two decimal places, the seasonalized forecast for February 2016 is approximately:
\[ \boxed{354.61} \]