Question

the new amazon warehouse on i-25 stores educational products in wing g. storage bins in this wing are specified by their aisle, location in the aisle, and shelf. there are 50 aisles, 85 horizontal locations in each aisle, and 5 shelves throughout the wing. what is the least number of products the company can have so that at least two products must be stored in the same bin?

Answer 1

To ensure at least two products are stored in the same bin in the described Amazon warehouse, we need one more product than the total number of bins available. Calculating the total bins as 50 aisles × 85 locations × 5 shelves = 21,250 bins, the answer is 21,251 products.

Step-by-step explanation:

To find the least number of products the company can have so that at least two products must be stored in the same bin, we should consider the Pigeonhole Principle. The principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item.

In the Amazon warehouse example provided, we have 50 aisles with 85 locations in each aisle, and 5 shelves at each location. To find the total number of bins, we multiply these numbers together:

1. 50 aisles × 85 locations/aisle = 4,250 locations.
2. 4,250 locations × 5 shelves/location = 21,250 bins.

Following the Pigeonhole Principle, to guarantee that at least one bin contains two products, we need 21,251 products, since having 21,250 products could mean each bin has exactly one product.

Amazon, known for its economies of scale and computerized warehouses, makes use of such principles to maximize efficiency in storing and managing their vast inventory of products, from educational products to virtually any type of goods.