Problem $20-19($Algo$)$

The annual demand for a product is $16,000$ units. The weekly demand is $308$ units with a standard deviation of $80$ units. The cost to place an order is $$30\mathrm{.}50,$ and the time from ordering to receipt is six weeks. The annual inventory carrying cost is $$0\mathrm{.}10$ per unit.

a$.$ Find the reorder point necessary to provide a $95$ percent service probability. $($Use Excel's NORMSINV$()$ function to find the correct critical value for the given $a-$level. Round $"z"$ value to $2$ decimal places.$)$

Answer is complete but not entirely correct.

Reorder point

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 new service probability be$?($Use Excel's NORMSDIST$)$ function to find the correct probability for your computed Z$-$value. Round $"z"$ value to $2$ decimal places and final answer to $1$ decimal place.$)$

Answer is complete and correct.

Service probability

$79\mathrm{.}4$

$\%$