A restaurant serving chicken legs orders from a butcher for $9/b. The butcher charges the restaurant a set fee of $60 for shipping and delivery. The restaurant stores the chicken legs in its freezer with the inventory carrying rate of 20%. The restaurant estimates that informing the guests they ran out of chicken legs and have to order something else results in $3 lost profit. The normally distributed data shows a mean of chicken legs lbs ordered per day is 50lbs, with a standard deviation of 15lbs. In the past, the butcher missed delivery days, but the owner of the restaurant found that the average (mean) time between placing and order and delivery is 5 days, and the standard deviation is 2 days. A)How many lbs of chicken legs should the restaurant should order each time and when should it place its orders to minimize the total average annual holding, shipment, and shortage cost? B) Find the mean time 1lb of chicken legs is in the freezer before being served. C) If the restaurant wants to reduce the number of people who have to pick another dish (when the chicken is out) to 5%, what's the optimal ordering policy, and what is the safety inventory with this policy? D) Because of the size of the freezer, the restaurant can only order 500lbs max each time. Use this constraint to resolve part a