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 $$11\mathrm{.}50$ per bag. The following information is available about these bags. Refer to the standard normal table for $z-$values.

$>$ Demand $=95$ bags$/$week

$>$ Order cost $=$$$\frac{58}{?}$ order

$>$ Annual holding cost $=28$ percent of cost

$>$ Desired cycle$-$service level $=92$ percent

$>$ Lead time $=1$ week$($s$)(7$ working days$)$

$>$ Standard deviation of weekly demand $=10$ bags

$>$ Current on$-$hand inventory is $315$ bags, with no open orders or backorders.

a$.$ What is the EOQ?

Sam's optimal order quantity is $422$ bags. $($Enter your response rounded to the nearest whole number.$)$

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

The average time between orders is $4\mathrm{.}4$ weeks. $($Enter your response rounded to one decimal place.$)$

b$.$ What should $R$ be$?$

The reorder point is $$ bags. $($Enter your response rounded to the nearest whole number.$)$

c$.$ An inventory withdrawal of $10$ bags was just made. Is it time to reorder?

It $$ time to reorder.

d$.$ The store currently uses a lot size of $505$ bags $($i$.$e$.,Q=505).$ What is the annual holding cost of this policy?

The annual holding cost is $$813\mathrm{.}05.($Enter your response rounded to two decimal places.$)$

What is the annual ordering cost?

The annual ordering cost is : $($Enter your response rounded to two decimal places.$)$