Southern Fresh has decided to make a policy that every product will receive enough shelf space to ensure that 98.75 percent of customers will find that their first choice is available. Consider Hot Bull corn chips. Demand is normally distributed. Average daily demand for this is product 55, with a standard deviation of 30. Bags of Hot Bull chips can be stacked 20 deep per facing. (A facing is the width on a shelf required to display one item of a product) Deliveries from Southern Fresh's central warehouse occur two days after a store manager submits an order. 

Per Professor: am getting several clarification question on problem 13.10.  essentially part (a) asks for the order-up-to level (in facings) to satisfy a fill rate of 98.75% while part (b) asks for the order-up-to level (in facings) to satisfy an instock probability of 98.75%.

A. How many facings should Southern Fresh allocate to Hot Bull corn chips?

B. How many facings are needed to achieve a 98.75 percent in-stock probability?

C. Suppose Southern Fresh allocates 11 facings to Hot Bull corn chips. On average, how many bags of Hot Bull are on the shelf at the end of the day?

D.    Although Southern Fresh does not want to incur the cost of holding inventory, it does want to leaver customers with the impression that it is well stocked. Hence, Southern Fresh employees continually roam the isles of the store to adjust the presentation of the product. In particular, they shift product around so that there is an item in each facing whenever possible. Suppose Southern Fresh allocates 11 facings to Hot Bull corn chips. What is the probability that at the end of the day there will be an empty facing, that is, a facing without any product?