Develop and answer in detail the following exercises:

1) A coffee shop sells Colombian coffee at a constant rate of 280 per year. The beans are purchased from a local supplier for $2.40 per pound. The coffee shop estimates that it costs $45 to place a coffee order, between stationery and labor time, and that inventory holding costs are based on an annual interest rate of 20%.

a) Calculate the optimal order quantity for Colombian coffee.

b) What is the time between orders?

c) What is the average annual cost of holding inventory and setup due to this item?

d) If the replenishment lead time is 3 weeks, calculate the reorder level, based on available inventory, 52 weeks a year are worked.