an online retailer uses a fixed time period with safety stock inventory system to control the inventory of a type of visual reality (VR) headsets it stocks. Demand for the VR headsets average 50 units per day and the standard deviation of the daily demand is 9 units. The retailer reviews the amount on hand and places an order once a month (i.e., every 30 days). the lead time is 14 days.

a. the retailer wants the probability of no stockout at the end of an inventory cycle to be 99% (i.e., cycle service level = 0.99). calculate the target level for inventory position that should be used when determining order size.

b. today, the retailer has reviewed this item and found 250 units of VR headsets on hand and 120 units on order from the supplier. how many units should the online retail store order today?