Given the following information, formulate an inventory management system. The item is demanded $50$ weeks a year.

PARAMETER

VALUE

Item cost $ $$11\mathrm{.}00$

Order cost $$257\mathrm{.}00$ per order

Annual holding cost $32\%$ of item cost

Annual demand $26,900$ units

Average weekly demand $538$ per week

Standard deviation of

weekly demand

Lead time

Service probability

$30$ units

$1$ week

$90\%$

a$.$ Determine the order quantity and reorder point.

Note: Use Excel's NORMSINV$()$ function to find the correct critical value for the given a$-$level. Do not round intermediate

calculations. Round $"z"$ value to $2$ decimal places and final answer to the nearest whole number.

b$.$ Determine the annual holding and order costs.

Note: Do not round any intermediate calculations. Round your final answers to $2$ decimal places.