Echo Electronics is a retailer of hand held texting devices. You are in charge of inventory control for one of Echo's most profitable multitasking devices (MT-46). Weekly demand for the MT-46 varies, with an average of 34,500 units and a standard deviation of 75 units. The MT-46 is purchased from a wholesaler at a cost of $99.50 per unit. The supply lead time is six weeks. Placing an order costs $620, and the inventory carrying rate per year is 45 percent of the item's cost. Echo operates five days per week, 50 weeks per year.
a. What is the optimal ordering quantity for the MT-46?
b. How many units of the MT-46 should be maintained as safety stock for 97.5 percent protection against stock outs during an order cycle?
c. If supply lead time can be reduced to three weeks, what is the percentage reduction in the number of units maintained as safety stock for the same 97.5 percent stock out protection?
d. If, through appropriate sales promotions, the demand variability is reduced so that the standard deviation of weekly demand is 25 units instead of 75, what is the percentage reduction (compared to that in part b) in the number of units maintained as safety stock for the same 97.5 percent stock out protection?