Here $is$ Problem $4$: Sam$s$ Cat Hotel operates $52$ weeks per year, $6$ years 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$=90$ bag$\frac{s}{w}$eek

Order Cost$=$ $$\frac{54}{o}$rder

Annual holding cost$=27$ percent $ofcost$

Desired cycle$-$service level$=80$ percent

Lead time$=3$ weeks $(18$ working days$)$

Standard deviation $of$ weekly demand$=15$ days

Current $on-$hand inventory $is320$ bags, with $no$ open orders $or$ backorders

Suppose that Sam's Cat Hotel $in$ Probler $4$ uses $aP$ system instead $ofaQ$ system. The

average daily demand $isd=\frac{90}{6}=15$ bags and the standard deviation $of$ deily demand

$is{}_d=\frac{{}_{\text{s}\text{e}\text{a}\text{t}}}{\sqrt[\phantom{2}]{6}}=(\frac{15}{\sqrt[\phantom{2}]{6}})=6\mathrm{.}124$bags.

$a.$ What $P(in$ working days$)$ and $T$ should $be$ used $to$ approximate the cost trade$-$offs

$of$ the EOQ $?$

$b.$ How much more safety stock $is$ needed than with $aQ$ system?

$c.Itis$ time for the periodic review. How much kitty litter should $be$ ordered?