Sam$$s Cat Hotel operates $52$ weeks per year, $7$ days per week, and uses a continuous review inventory system. It purchases Kitty Litter for $$16\mathrm{.}48$ per bag. The following information is available about these bags:

Demand $135$ bags$/$week

Order Cost $$75\mathrm{.}50$ per order

Annual Holding Cost $28\mathrm{.}50\%$ of cost

Desired Cycle$-$Service Level $80\%$

Lead Time $3$ weeks $(21$ working days$)$

Standard Deviation of weekly demand $21$ bags

Current on Hand Inventory $440$ bags

Open Orders or Backorders $0$