The demand for a product is normally distributed with a mean of $3,000$ items per year and a standard deviation of $400.$ Each item costs $$200$ and the ordering cost is $$100.$

The lead time is $1$ week while there are $50$ working weeks in a year. The specialists estimated the stockout cost of approximately $$250$ per item. Carrying rate is $25\%.$

If the maximum stockout probability is aimed to be $1\%,$ and the service level is $98\%,$ answer questions $1-8.$

$1.$ What is the economic order quantity?

$($a$)553\mathrm{.}1152\mathrm{.}6$

$($c$)148\mathrm{.}7$

$($d$)131\mathrm{.}9$

$2.$ What is the standard deviation of demand during the lead time?

$($a$)56\mathrm{.}57$

$($b$)95\mathrm{.}36$

$($c$)83\mathrm{.}25$

$($d$)64\mathrm{.}35$

$3.$ Find the safety stock with the maximum stockout probability method.

$($a$)93\mathrm{.}05$

$($b$)58\mathrm{.}35$

$($c$)46\mathrm{.}36$

$($d$)26\mathrm{.}97$

$4.$ Find the reorder point with the maximum stockout probability method.

$($a$)193\mathrm{.}05$

$($b$)136\mathrm{.}62$

$($c$)463\mathrm{.}23$

$($d$)352\mathrm{.}43$

$5.$ Find the safety stock with the average service level $($fill rate$)$ method.

$($a$)35\mathrm{.}32$

$($b$)56\mathrm{.}84$

$($c$)45\mathrm{.}37$

$($d$)47\mathrm{.}52$

$6.$ Find the reorder point with the averge service level $($fill rate$)$ method.

$($a$)573\mathrm{.}25$

$($b$)147\mathrm{.}52$

$($c$)67\mathrm{.}42$

$($d$)174\mathrm{.}35$

$7.$ Find the safety stock with the stockout cost method.

$($a$)28\mathrm{.}28$

$($b$)34\mathrm{.}73$

$($c$)75\mathrm{.}35$

$($d$)46\mathrm{.}35$

$8.$ Find the reorder point with the stockout cost method.

$($a$)324\mathrm{.}85$

$($b$)146\mathrm{.}94$

$($c$)245\mathrm{.}33$

$($d$)128\mathrm{.}28$