Final answer:
Using the Pigeonhole Principle, the least number of products needed to ensure at least two products are stored in the same bin is one more than the total number of storage bins. With 50 aisles, 85 locations per aisle, and 5 shelves, this amounts to 21251 products. The correct answer is 21251.
Step-by-step explanation:
To determine the least number of products the company can have so that at least two products must be stored in the same bin, we can use the Pigeonhole Principle. This principle states that if there are more pigeons than pigeonholes, at least one pigeonhole must contain more than one pigeon. In this analogy, 'products' are pigeons and 'storage bins' are pigeonholes.
The total number of unique storage bin locations can be calculated by multiplying the number of aisles by the number of locations in each aisle and then by the number of shelves. Therefore, it would be 50 aisles multiplied by 85 locations per aisle, and then by 5 shelves, which is 50 * 85 * 5.
The calculation gives us:
50 * 85 * 5 = 21250
This is the total number of storage bins available. To guarantee that at least two products are in the same bin, one more product than the total available bins would be needed. Hence, the least number of products would be:
21250 + 1 = 21251
The correct answer, therefore, is 21251 products, which is the minimum number required to ensure that at least two products are stored in the same bin.