Consider a periodic review system, where orders are placed every $20$ days. The firm strives to provide a $94\mathrm{.}84\%$ cycle service level. Demand averages $430$ units per day, and the standard d of demand per day is $104$ units. Lead time is $11$ days $($round $Z-$values, standard deviations to two decimal places$).$

a$.$ How many units of safety stock should be held? $$ units $($round your response to the nearest integer$).$

b$.$ What should the target inventory level $($order$-$up$-$to level$)$ be$?$ units $($round your response to the nearest integer$).$

c$.$ Suppose that it is time to review the item. There are $187$ units in inventory, and there is an outstanding backorder for $421$ units. An order for $123$ units is on the way. How many units should ordered now? $$ units $($round your response to the nearest integer$).$