$3.$ Joe henry$$s machine shop uses $2,500$ brackets during the course of a year. These brackets are purchased from a supplier $90$ miles away.the following information is known about the brackets:

Annual demand: $4,200$

Holding cost per bracket per year:$$1\mathrm{.}50$

Order cost per order: $$18\mathrm{.}75$

Lead time: $3$ years

Working days per year: $250$

i$)$ What is the EOQ?

ii$)$ What is the average inventory if the EOQ is used? What would be the annual inventory holding cost?

iii$)$ What is the optimal number of orders per year? What would be the annual order cost?

iv$)$ What is the total annual cost of managing the inventory?

v$)$ What is the optimal number of days in between any two orders?

vi$)$ What is the reorder point$($ROP$)?$