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?

A$)$ For a $95$ Percent Case Fill Rate:

B$)$ For a $99$ Percent Case Fill Rate:

C$)$ For Daily Replenishment with a $99$ Percent Fill Rate: