Annual demand for a product is $10,400$ units; weekly demand is $200$ units with a standard deviation of $60$ units. The cost of placing an order is $$125,$ and the time from ordering to receipt is four weeks. The annual inventory carrying cost is $$0\mathrm{.}80$ per unit. To provide a $90$ percent service probability, what must the reorder point be$?$ Annual demand for a product is $10,400$ units; weekly demand is $200$ units with a standard deviation of $60$ units. The cost of placing an order is $\backslash (\backslash$$ $125\backslash ),$ and the time from ordering to receipt is four weeks. The annual inventory carrying cost is $\backslash (\backslash$$ $0\mathrm{.}80\backslash )$ per unit.

a$.$ To provide a $90$ percent service probability, what must the reorder point be$?$

Note: Use Excel's NORMSINV$()$ function to find the correct critical value for the given $\backslash (\backslash$alpha $\backslash )-$level. Do not round intermediate calculations. Round $"\backslash ($ z $\backslash )"$ value to $2$ decimal places and final answer to the nearest whole number.

units

b$.$ Suppose the production manager is told to reduce the safety stock of this item by $110$ units. If this is done, what will the new service probability be$?$

Note: Use Excel's NORMSDIST$()$ function to find the correct probability for your computed Z$-$value. Round your answer to the nearest whole number.

Service probability $\backslash \%$