Consider a periodic review system, where orders are placed every $19$ days.

The firm strives to provide a $94\mathrm{.}84\%$ cycle service level. Demand averages

$420$ units per day, and the standard deviation of demand per day is $107$

units. Lead time is $13$ 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 $174$ units

in inventory, and there is an outstanding backorder for $416$ units. An order

for $126$ units is on the way. How many units should be ordered now?

units $($round your response to the nearest integer$).$