Ollah's Organic Pet Shop sells about $4,750$ bags of free$-$range dog biscuits every year. The fixed ordering cost is $$27,$ and the cost of holding a bag in inventory for a year is $$3\mathrm{.}75.$

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a$.$ What is the economic order quantity for the biscuits?

The EOQ is $($Enter your response rounded to the nearest whole number.$)$

b$.$ Suppose Ollah decides to order $160$ bags at a time. What would the total ordering and holding costs for the year be$?($For this problem, don't consider safety stock when calculating holding costs.$)$

The total ordering and holding costs are $

$($Enter your response rounded to the nearest dollar.$)$

c$.$ Average weekly demand for free$-$range dog biscuits is $81$ bags per week, with a standard deviation of $11$ bags. $($bllah uses a continuous inventory review system to manage inventory of the biscuits. Ollah wants to set the reorder point high enough that there is only a $0\mathrm{.}1\%$ chance of running out before the next order comes in$.$ Assuming that the lead time is a constant $3$ weeks, what should the reorder point be$?$

The reorder point is bags. $($Enter your response rounded to the nearest whole number.$)$

d$.$ Suppose Ollah decides to use a periodic review system to manage the free$-$range dog biscuits, with the vendor checking inventory levels every week. Under this scenario, what would the restocking level be$,$ assuming the same demand and lead time characteristics listed in part c$.$ and the same $99\mathrm{.}9\%$ service level? $($Note that because the standard deviation of weekly demand is $11,$ basic statistics tells us the standard deviation of demand over $4$ weeks will be $22.)$