Question 1. (50 Points) Deep Six Seafood is a fresh Maine lobster distributor located in Tempe, AZ. The daily demand in the Arizona region for lobsters is approximately Normally distributed with a mean of 50 and standard deviation of 12. Deep Six pays $10 for each lobster they buy from the supplier in Maine. Air freight charges have increased significantly, and it now costs Deep Six $150 to place an order. Because the lobsters are shipped live in a saltwater tub, the order cost is not affected by the order sizes. The cost to keep a lobster alive until needed runs about $0.02 per day. In case a restaurants demand cannot be satisfied on time due to an out-ofstock situation, Deep Six still delivers this particular order at a later time as soon as possible, but offers a $1 discount per lobster on its sale price. The management also believes that there is a $2 cost of loss-of-goodwill for each out-of-stock demand. The replenishment lead time is three days, including the flight time and the transportation times from the supplier to the Maine Airport and from Phoenix Airport to Deep Six in Tempe. a) (15 Points) If Deep Six decides to employ an policy, what should be the optimal policy parameters? b) (10 Points) What are the safety stock level and the Type I service level achieved under this policy? c) (10 Points) What is the total expected cost per day incurred by implementing this policy? d) (10 Points) The Maine supplier is willing to give Deep Six a $0.5 discount on each lobster if orders are placed in lots of 1000 each. Should Deep Six accept this offer? e) (5 Points) If the owner of Deep Six asserts to satisfy their customers 98% of the time, what should be the optimal policy parameters? What is the safety factor, in this situation?