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

PARAMETER VALUE

Item cost $ $12\mathrm{.}00$

Order cost $ $194\mathrm{.}00$ per order

Annual holding cost $21\%$ of item cost

Annual demand $24,700$ units

Average weekly demand $494$ per week

Standard deviation of weekly demand $20$ units

Lead time $2$ week

Service probability $95\%$

Determine the order quantity and reorder point.

Note: Use Excel's NORMSINV$()$ function to find the correct critical value for the given $\backslash$alpha $-$level. Do not round intermediate calculations. Round $"$z$"$ value to $2$ decimal places and final answer 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 $$55$ per order was offered for purchase quantities of $2,000$ or more units per order. If you took advantage of this price break, how much would you save annually?

Note: Do not round any intermediate calculations $($including number of setups per year$).$ Round your final answer to $2$ decimal places.