Consider a periodic review$$ system, where orders are placed every $22$ days. The firm strives to provide a $95\mathrm{.}05\%$ cycle service level. Demand averages $415$ units per$$ day, and the standard deviation of demand per day is $107$ units. Lead time is $11$ days$($round Z$-$values, standard deviations to two decimal$$ places$).$

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Part $1$

a$.$ How many units of safety stock should be$$ held?

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

b$.$ What should the target inventory level$($order$-$up$-$to level$)$ be$?$

$$

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

c$.$ Suppose that it is time to review the item. There are $171$ units in$$ inventory, and there is an outstanding backorder for $433$ units. An order for $119$ units is on the way. How many units should be ordered$$ now?

$$

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