We are given the following information about a product: Cost of placing an order $$100$ Cost per item $$5$ Sale price per item $$8$ Annual holding cost $40\%$ of cost of item Annual demand $5,000$ units Lead time demand $N(20,900)$

a$)$ If the reorder point that minimizes expected cost is $80,$ what is the shortage cost? $($Assume backlogging.$)$

b$)$ If the reorder point that minimizes expected cost is $80,$ what is the shortage cost? $($Assume lost sales.$)$

c$)$ What reorder point would meet $90\%$ of all demand on time?

d$)$ What reorder point would result in a stockout occurring during an average of $0\mathrm{.}5$ lead time per year.