We predict that we will have a weekly demand for books that are normally distributed with mean 10 and variance 49). N(10,49). It takes 2 weeks for an order to arrive at a bookstore. To ship the order and the fixed cost comes to about $80. Each book cost $2.00. We have a holding cost of 25% based on an annual rate. The estimated cost from the loss of customer goodwill for not being able to provide a book when requested would be $25.00 (the unit stockout cost).

(1) Find the optimal (Q,R) policy that we should implement.

(2) Find the average frequency of ordering, fill rate, backorder level and inventory level for the policy you found in part (1).

(3) Suppose that book producer decided to require an order size of 1000 books. Find the reorder level that we should use if we want to satisfy 99% (meaning 99% fill rate) of our customer demands for books.