Problem $17-10$

The annual demand for a product is $15,600$ units. The weekly demand is $300$ units with a standard deviation of $90$ units. The cost to place an order is $$31\mathrm{.}20,$ and the time from ordering to receipt is four weeks. The annual inventory carrying cost is $$0\mathrm{.}10$ per unit.

$($a$)$ Find the reorder point necessary to provide a $98$ percent service probability. $($Round your answer to the nearest whole number.$)$

Reorder point $1,569+-1$ units

$($b$)$ Suppose the production manager is asked to reduce the safety stock of this item by $50$ percent. If she does so$,$ what will the nehi service probability be$?($Round your answer to $1$ decimal place. Omit the $"\%"$ sign in your response.$)$

Service probability