AM-GM Any Baby’s BMs

Abstract

Reusable diapers are growing in popularity due to new and improved designs. The total cost associated with reusable diapers is the sum of the upfront cost of purchasing the diapers and the reoccurring cost of cleaning the diapers. With a nice application of the AM-GM inequality we show that the minimum cost to the consumer is twice the geometric mean of the upfront and cleaning costs plus the cost of a single reusable diaper. Moreover, the minimum is obtained when the upfront cost is equal to the total cleaning costs plus the cost of a single reusable diaper. We conclude with an analysis of our reusable diaper model and a cost comparison with disposable diapers.