A company stocks a component that costs $25 per unit. Annual usage of this item is expected to be 2184 units. The firm is open for business 52 weeks per year, so weekly demand is 42 units per week, with a standard deviation of 18 units. The firm's cost accountants have estimated that it costs $40 every time an order is placed for more components, and that carrying the item in inventory costs about $10 per unit per year. Past experience with their supplier indicates that the time from ordering more items to receipt of the shipment of those items is 14 days (assume that they are open 7 days per week.)
a. What quantity should be ordered each time? (Assume that the EOQ assumptions apply.)
b. What is the minimum total annual cost (ordering + holding + purchase) for managing this inventory item?