To determine the three-period weighted moving average for the next time period, we need to consider the monthly profits of the three most recent months and apply the given weights to them. The weights are assigned as follows: 3 for the most recent month, 2 for the second most recent month, and 1 for the third most recent month.
Here, the three most recent months along with their respective profits are:
- August 2014 (Aug-14): \[tex]$18,457
- July 2014 (Jul-14): \$[/tex]19,142
- June 2014 (Jun-14): \[tex]$17,200
Step-by-step solution:
1. Assign the weights:
- Most recent month (Aug-14): weight is 3
- Second most recent month (Jul-14): weight is 2
- Third most recent month (Jun-14): weight is 1
2. Multiply each month's profit by its respective weight and then sum the results:
\[
\text{Weighted sum} = (18,457 \times 3) + (19,142 \times 2) + (17,200 \times 1)
\]
3. Calculate the weighted sum:
\[
(18,457 \times 3) + (19,142 \times 2) + (17,200 \times 1) = 55,371 + 38,284 + 17,200 = 110,855
\]
4. Calculate the total weight:
\[
\text{Total weight} = 3 + 2 + 1 = 6
\]
5. Compute the weighted moving average by dividing the weighted sum by the total weight:
\[
\text{Weighted moving average} = \frac{110,855}{6} = 18,475.8333
\]
6. Round the result to one decimal place:
\[
18,475.8333 \approx 18,475.8
\]
Therefore, the three-period weighted moving average for the next time period is \$[/tex]18,475.8.
