Problem $12-26($Static$)$

A small copy center uses five $500-$sheet boxes of copy paper a week. Experience suggests that usage can be well approximated by a normal distribution with a mean of five boxes per week and a standard deviation of one$-$half box per week. Two weeks are required to fill an order for letterhead stationery. Ordering cost is $$2,$ and annual holding cost is $20$ cents per box.

Use Table.

a$.$ Determine the economic order quantity, assuming a $52-$week year. $($Round your answer to the nearest whole number.$)$

b$.$ If the copy center reorders when the supply on hand is $12$ boxes, compute the risk of a stockout. $($Round $"$z$"$ value to $2$ decimal places and final answer to $4$ decimal places.$)$

c$.$ If a fixed interval of seven weeks is used for ordering instead of an ROP, how many boxes should be ordered if there are currently $12$ boxes on hand, and an acceptable stockout risk for the order cycle is $\mathrm{.}0228?($Round $"$z$"$ value to $2$ decimal places and final answer to the nearest whole number.$)$