You are in charge of inventory control of a highly successful product retailed by your firm. Weekly demand for this item? varies, with an average of 150 units and a standard deviation of 25 units. It is purchased from a wholesaler at a cost of ?$15.00 per unit. The supply lead time is 9 weeks. Placing an order costs ?$48.00 and the inventory carrying rate per year is 18 percent of the? item's cost. Your firm operates 5 days per? week, 48 weeks per year. Refer to the standard normal table for? z-values.

a. What is the optimal ordering quantity for this? item?

units. ?(Enter your response rounded to the nearest whole? number.)

b. How many units of the item should be maintained as safety stock for 96 percent protection against stockouts during an order? cycle?

units. ?(Enter your response rounded to the nearest whole? number.)

c. If supply lead time can be reduced to1 ?weeks, what is the percent reduction in the number of units maintained as safety stock for the same 96 percent stockout? protection?

?(Enter your response rounded to two decimal? places.)

d. If through appropriate sales? promotions, the demand variability is reduced so that the standard deviation of weekly demand is 6 units instead of 25?, what is the percent reduction? (compared to that in part? (b)) in the number of units maintained as safety stock for the same 96 percent stockout? protection?

?(Enter your response rounded to two decimal? places.)