Your firm is planning to introduce a new product line. Your task is to determine the inventory implications of the new product. The typical product will ship an average of $25$ units per day from the firm$$s central DC$.$ Historical sales patterns indicate that the standard deviation of daily sales should be approximately $3.$ The typical performance cycle for comparable products has been a mean of seven days and a standard deviation of $2.$ A$)$ Assuming a replenishment quantity from the plant of $300$ units, what are the safety stock and resulting average inventory for a $95$ percent case fill rate? B$)$ What are the inventory implications $($safety stock and average inventory$)$ of increasing the case fill rate objective to $99$ percent? C$)$ What would be the inventory implications for daily replenishment with a $99$ percent fill rate objective, assuming that the same level of demand and performance cycle uncertainty is maintained?