$$Sam$\text{'}$s Pet Hotel operates $52$ weeks per$$ year, $5$ days per$$ week, and uses a continuous review inventory system. It purchases kitty litter for $$$$11\mathrm{.}50$ per bag. The following information is available about these bags. Refer to the standard normal tableLOADING... for$$ z$-$values.

Demand $=100$bags$/$week

Order cost$=$$$58/$order

Annual holding cost$=29$ percent of cost

Desired $$cycle$-$service level $99$ percent

Lead time$=4$week$($s$)(200$ working$$ days$)$

$16$ Standard deviation of weekly demand$=$ bags

Current $$on$-$hand inventory is $310$bags$,$ with no open orders or backorders.

Part $2$

a$.$ What is the$$ EOQ?

$$Sam$\text{'}$s optimal order quantity is

$$

enter your response here bags. $($Enter your response rounded to the nearest whole$$ number.$)$