Each day on average, a mother needs 10 diapers. The mother orders diapers from the a company. The company produces a diaper at a cost of $1 per diaper, and it sells at a price of $2 per diaper. The company charges $4 shipping fee per shipment regardless of the order size. It takes 9 days for each shipment to be delivered to the customer. 1 year = 360 days. It is estimated that the aggregate holding cost for diapers, inclusive of the physical holding costs and cost of capital, is 25% per year.
1. What is the mother’s optimal order quantity of diapers per each order? What is the optimal order quantity per each order?
2. The Company provides express shipping, a shipping period of 1 day instead of 9 days, at the same shipping fee of $4 per shipping for premium customers. These customers have to pay an annual membership fee of $5. Explain the trade-off that the mother should analyze when deciding whether she should become a premium customer.