From past experience, it appears that demand for an item is $3,075$ units$/$year$.$ The ordering cost is $$50,$ the basic price of the item is $$2,$ and an r value of $0\mathrm{.}20$ $$/$$$/$year is used. What is the time between replenishments from a supplier in weeks $($a year is $50$ weeks$),$ if the supplier delivers with the rate of $4,000$ units$/$year$?$ What order quantity should be used?

If the manufactuer naively uses simple EOQ methods for the order quantity, determine the penealty percentage they should pay due to that mistake?