Final answer:
The length of the inventory period is approximately 44.57 days.
Step-by-step explanation:
The length of the inventory period can be determined using the formula:
Inventory Period = (Average Inventory / Cost of Goods Sold) x 365 days
First, we need to calculate the average inventory:
Average Inventory = (Beginning Inventory + Ending Inventory) / 2
Substituting the given values into the formula:
Average Inventory = ($42,000 + $57,000) / 2 = $99,500
Next, we can calculate the inventory period:
Inventory Period = ($99,500 / $811,800) x 365 days = 44.57 days
Therefore, the length of the inventory period is approximately 44.57 days.