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

Standard deviation of weekly demand $=15$ bags

Order cost $=$ $$54$ per order

Annual Holding cost $=27\%$ of cost

Desired cycle$-$service level $=80\%$

Lead time $=3$ weeks

$($Note : Exclude costs due to Safety Stock for all the questions in this problem$)$

What is the Reordering point

Suppose that actual demand is $60$ bags but that ordering costs are cut to only $$6$ by using the internet to automate order placing. However, the buyer does not tell anyone, and the EOQ is not adjusted to reflect this reduction in $"$S$".$ What is the cost penalty for not updating the EOQ?