Elvis' Cat Hotel operates $52$ weeks per year, $6$ days per week, and uses a continuous review inventory system. It purchases kitty litter for $$20$ per bag. The following information is available about these bags.

Demand $=180$bags$/$ week

Order cost $=$$$45/$ order

Annual holding cost $=15$ percent of cost

Lead time $=2$ weeks $(12$ working days$)$

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

b$)$ The store currently uses a lot size of $900$ bags $($i$.$e$.Q=900).$ What is the annual holding cost? Annual ordering cost? Without calculating the EOQ, how can you conclude from these two calculations that the current lot size is too large?

c$)$ What would be the annual cost saved by shifting from the $900-$bag lot size to the EOQ?