Demand for strawberry smoothies can be approximated by a normal distribution with a mean of $50$ liters per week and a standard deviation of $8$ liters per week. The new manager desires a service level of $97$ percent. Lead time is two days, and the caf$$ is open seven days a week. $($Hint: Work in terms of weeks.$)$ a$.(50$ pts$)$ If a Reorder Point $($ROP$)$ model is used, what ROP would be consistent with the desired service level?

b$.(50$ pts$)$ If a fixed$-$interval $($periodic review$)$ model is used instead of an ROP model, what order size would be needed for the $92$ percent service level with an order interval of $14$ days and a supply of $12$ liters on hand at the order time?