A product has an average weekly demand of $75$ with an EOQ of $300.$ The lead time is $2$ weeks. The inventory holding cost is $$2$ per unit per week. The shortage cost is $$18$ per unit over the order cycle. The demand forecast error follows

$(0,25^2)$ each week.

$($a$)(1$ pt$)$ What is the safety stock needed to mitigate the risk of high demand?

$($b$)(0\mathrm{.}5$ pts$)$ It is proposed to reduce the lead time to $1$ week. This will cost $$50$ per order cycle. Does the reduction in safety stock inventory cost per order cycle justify this cost?