Consider the following information for inventory management. The item is demanded $50$

weeks a year. $(2$ weeks of holiday$)$

Item cost $$10\mathrm{.}00($per unit$)$

Order cost $$250\mathrm{.}00($per order$)$

Annual holding cost $33\%$ of item cost per year

Lead time $1$ week

Average demand $25,750($units$/$year$)$

Suppose that demand is random, and the standard deviation of weekly demand is $25.$ The

management$$s target service level is $95\%.$

$($a$)$ State the optimal order quantity and reorder point.

$($b$)$ Determine the annual holding and ordering costs.