Soap and Towels 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 choosing base stock levels. Weekly demand for a merino towel can be modeled with a Poisson distribution with mean 1.2. 

a. Say they operate with a base stock level of 6. What is their expected on-hand inventory?

b. Say they operate with a base stock level of 7. What is their in-stock probability? 

c. Say they operate with a base stock level of 8. What is their average on-order inventory? 

d. Say they wish to have an in-stock probability of 0.97. What base stock level should they select?