Arthur manages inventory levels at pizza restaurant where demand for pizzas is normally distributed with a mean of $80$ pizzas per day and a standard deviation of $21\mathrm{.}6$ pizzas per day. Arthur desires a service level of $97\mathrm{.}5\%.$ Lead time is $6$ days, and the restaurant is open seven days a week, $365$ days a year.

Each pizza costs $$8\mathrm{.}50$

Lost sales are valued at $$2\mathrm{.}50$

Every order to the supplier costs $$15$

Annual holding costs are $5\%$ the cost of inventory

A$.$ Calculate the EOQ of purchasing from the supplier.

B$.$ If an ROP model is used, what ROP would be consistent with the desired service level?

C$.$ What is the annual cost of lost'sales?

D$.$ What is the total annual shortage cost?