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{.}38$ per bag. The following

information is available about these bags.

Demand $125$ bags$/$week

Order Cost $$75\mathrm{.}00$ per order

Annual Holding Cost $27\%$ 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 $450$ bags

Open Orders or Backorders $0$

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