S&T is a retailer of home goods. They receive inventory from their supplier with a 2-week lead time. Assume they order weekly, and they use the order-up-to model for managing inventories. A peppermint soap sells on average one box every 5 weeks. AssumeS&T's demand is Poisson distributed.'

D) Suppose due to recent global supply chain disruptions, S&T's supplier increases the lead time to three weeks. Given the additional risks posed by global supply chain disruptions, S&T decides to increase its order-up-to level to 2 boxes. What is their stockout probability?

E) Given the new lead time (i.e., three weeks), suppose S&T wants to minimize inventory while achieving at least a 0.9875 in-stock probability for the peppermint soap. What order-up-to level (in boxes) should they use?

F) Given the new lead time (i.e., three weeks), suppose S&T uses an order-up-to level of 3 boxes. What is the expected on-order inventory?