A new logistics analyst has approached you regarding a potential problem. Her analysis indicates the cost of a back order is $$50$ for our Autographed Footballs, but she is not sure what the appropriate safety stock should be$.$ Given this back order cost, what probability of a stock out would be appropriate to use to manage the inventory levels?

Football cost $$200$

Annual Demand $5000$ units

Order Placement Costs per Order $$250$

Cost to hold the item per year $40\%$

Economic order quantity $177$

Lead Time $2$ weeks

Standard Deviation of Forecasted Demand During Lead Time $20$