In this problem, use marginal analysis to determine the optimal reorder point for the lost sales case. a Show that the average inventory level for the lost sales case may be written as ½ [(r - E(X) +...

In this problem, use marginal analysis to determine the optimal reorder point for the lost sales case. a Show that the average inventory level for the lost sales case may be written as

½ [(r - E(X) + E(B_r)) = (r - E(X) + E(Br) + q)]

 = r - E(X) + E(B_r) + q/2

b Although expected orders per year will no longer equal E(D)/ q (why?), we assume that the expected number of lost sales per year is relatively small. Thus, we may still assume that expected orders per year = E(D)/ q. Now use marginal analysis to derive (15).