Final answer:
Warehouse B is likely to carry more than 12,000 units but less than 24,000 units of inventory, as the inventory scales with the square root of the increase in demand, leading to approximately 16,970 units (none of the above options).
Step-by-step explanation:
The student's question deals with the inventory levels carried by warehouses A and B when considering customer demand and the square root law of cycle stocks. According to this law, when the customer demand doubles, the inventory does not double but increases by the square root of the increase in demand. Therefore, since Warehouse A carries an average of 12,000 units for a smaller region, and Warehouse B serves a region twice the size, we expect Warehouse B to carry more than 12,000 units but less than 24,000 units.
Specifically, the law implies that if you double the demand, the stock would increase by a factor of the square root of 2 (approximately 1.41). Thus, the inventory at Warehouse B is likely to be 12,000 units times the square root of 2, which equals approximately 16,970 units. So, the correct answer to the question would be (e) none of the above because 16,970 units is not less than 12,000, not equal to 12,000, not equal to 24,000, and not greater than 24,000 units. It's more than Warehouse A's inventory but less than if it had doubled.