AmerisourceBergen is one of the largest US wholesalers of prescription drugs. Currently, they require that all demand be met. However, they would like to determine whether they should consider allowing certain drugs to be backordered. They sell 40,000 packages of cytarabine, a chemotherapy drug, to health systems each year. It costs $27.10 to buy each package from the manufacturer, and they can be sold for $32.52 each. Because the cytarabine is perishable, the annual holding cost is fairly high, at 50% of the variable order cost. They estimate the backorder penalty to be $10 per package per year. Each order costs $10,000 to place, and there is no limit to the number of orders that can be placed each year. You can assume they can order partial (non-integer) packages.
Part A) Using the standard EOQ model without backorders, how many packages should AmerisourceBergen order at a given time? What would be their total annual cost?
Part B) If they decided to allow backorders, how many packages should they order each time an order is placed? How many units should they allow to be backordered? What would be the total annual cost?