To find the seasonalized forecast for Q1 of 2017, we need to first determine the value of \( t \) for Q1 2017 and then use the sales trend formula along with the seasonal factor for Q1.
Step 1: Determine the value of \( t \)
Since \( t = 1 \) corresponds to Q1 2015, we can calculate \( t \) for Q1 2017 as follows:
- Q1 2015: \( t = 1 \)
- Q2 2015: \( t = 2 \)
- Q3 2015: \( t = 3 \)
- Q4 2015: \( t = 4 \)
- Q1 2016: \( t = 5 \)
- Q2 2016: \( t = 6 \)
- Q3 2016: \( t = 7 \)
- Q4 2016: \( t = 8 \)
- Q1 2017: \( t = 9 \)
Thus, \( t = 9 \) for Q1 2017.
Step 2: Calculate the forecasted sales using the trend equation
The sales trend is given as:
\[ \text{Sales} = 7.00 \times t + 116.00 \]
Substituting \( t = 9 \):
\[ \text{Sales} = 7.00 \times 9 + 116.00 \]
Calculating that:
\[ \text{Sales} = 63.00 + 116.00 = 179.00 \]
Step 3: Apply the seasonal factor for Q1
From the information provided, the seasonal factor for Quarter #1 is \( 1.10 \). Now we apply this factor to the forecasted sales:
\[ \text{Seasonalized Forecast} = \text{Forecasted Sales} \times \text{Seasonal Factor} \]
Calculating the seasonalized forecast:
\[ \text{Seasonalized Forecast} = 179.00 \times 1.10 \]
Calculating that:
\[ \text{Seasonalized Forecast} = 196.90 \]
Final Result
The seasonalized forecast for Q1 of 2017 is 196.90.