Weekly demand for a certain product is normally distributed with mean $200$ and standard deviation $10.$ The source of supply is reliable and maintains a constant leadtime of $4$ week. Ordering cost is $$20$ per order, and annual inventory$-$holding cost is $$5$ per unit. Management wants to satisfy a $95\%$ probability of not running out of stock in any one ordering cycle. Assume $52$ weeks a year.

$($a$)$ What should be the reorder point? $($Note: The $z$ value corresponding to $95\%$ service level is $1\mathrm{.}65.)$

$($b$)$ What should the order quantity?