$.$ Sam$$s Cat Hotel operates $52$ weeks per year, $6$ days per week, and uses a continuous review

inventory system. It purchases kitty litter for $$11\mathrm{.}70$ per bag. The following information is

available about these bags.

Demand $=90$ bags$/$week

Order cost $=$ $$54/$order

Annual holding cost $=27$ percent of cost

Desired cycle$-$service level $=80$ percent

Lead time $=3$ weeks $(18$ working days$)$

Standard deviation of weekly demand $=15$ bags

Current on$-$hand inventory is $320$ bags, with no open orders or backorders.

a$.$ What is the EOQ? What would be the average time between orders $($in weeks$)?$

b$.$ What should R be$?$

c$.$ An inventory withdrawal of $10$ bags was just made. Is it time to reorder?

d$.$ The store currently uses a lot size of $500$ bags $($i$.$e$.,$ Q $=500).$ What is the annual holding cost

of this policy? Annual ordering cost? Without calculating the EOQ, how can you conclude from

these two calculations that the current lot size is too large?

e$.$ What would be the annual cost saved by shifting from the $500-$bag lot size to the EOQ?