Final answer:
To calculate moving averages for the manager's inventory, the sum of inventory levels for the respective 3-week, 5-week, or 7-week period is divided by the number of weeks in the period. This is done for each period as new data becomes available, helping the manager to determine the optimum forecasting method for inventory levels.
Step-by-step explanation:
To calculate the 3-week, 5-week, and 7-week moving averages for the warehouse manager's inventory, we will use the actual inventory data provided for the 10-week period and then extend the calculations to weeks 11 to 17 as new data points are available.
3-Week Moving Average Calculation
For week 4 (as an example), the 3-week moving average is the sum of the inventory levels for weeks 2, 3, and 4 divided by 3:
(98 + 96 + 109) / 3 = 101
This process is then repeated for each subsequent week, shifting the 3-week window forward one week at a time.
5-Week Moving Average Calculation
For week 6, the 5-week moving average is the sum of the inventory levels for weeks 2 through 6 divided by 5:
(98 + 96 + 109 + 104 + 129) / 5 = 107.2
Again, shift the 5-week window forward to calculate the next moving average.
7-Week Moving Average Calculation
For week 8, the 7-week moving average is the sum of the inventory for weeks 2 through 8 divided by 7:
(98 + 96 + 109 + 104 + 129 + 80 + 100) / 7 = 101.9
This 7-week moving average is then updated for each new week by shifting the window forward accordingly.
The manager can compare these moving averages to determine which provides the best balance between smoothness and responsiveness for forecasting the inventory levels.