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

PARAMETER VALUE

Item cost $$9\mathrm{.}00$

Order cost $$202\mathrm{.}00$ per order

Annual holding cost $28\%$ of item cost

Annual demand $24,000$ units

Average weekly demand $480$ per week

Standard deviation of weekly demand $20$ units

Lead time $1$ week

Service probability $90\%$

Determine the order quantity and reorder point.

Note: Use Excel$$s NORMSINV$()$ function to find your z$-$value and then round that z$-$value to $2$ decimal places. Do not round any other intermediate calculations. Round your final answers to the nearest whole number.

Determine the annual holding and order costs.

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

Assume a price break of $$50$ per order was offered for purchase quantities of $2,000$ units per order. If you took advantage of this price break, how much would you save annually?