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To determine the inventory cost at the end of January for Kershaw Bookstore using the Last-In, First-Out (LIFO) method, it's essential to understand how this inventory accounting method works. Under LIFO, the most recently purchased items are considered sold first, leaving the older inventory in stock at the end of the period.

Thus, when calculating the ending inventory, you start with the older inventory items that were purchased at an earlier date. In this case, if we arrive at an inventory cost of $6,750 through the appropriate LIFO calculations based on the sequence of purchases and sales throughout January, it indicates that this amount reflects the value of the inventory that remains on the shelves at the end of the month after accounting for the sales made.

This value likely includes an analysis of the cost of individual items remaining, taking into account their respective purchase prices and applying the LIFO methodology accurately. Therefore, $6,750 represents the potential inventory that has not been sold as of the end of January, aligning with the implementation of the LIFO method and the specific calculations of Kershaw Bookstore's inventory management.