A firm is faced with the attractive situation in which it can be obtain immediate delivery of item it stocks for retail sale. The firm has, therefore, not bothered to order the item in any systematic way. However, recently profits have been squeezed due to increasing pressures, and the firm has retained a management consultant to study its inventory management. The consultant has determined that the various costs associated with making an order for the item stocked are approximately $30 per order. She has also determined that the costs of carrying the item in inventory amount to approximately $20 per unit per year (primarily direct storage costs and foregone profit on investment in inventory). Demand for the item is reasonably constant over time and the forecast is for 19,200 units per year. When an order is placed for the item, the supplier immediately delivers the entire order to the firm. The firm operates 6 days a week plus a few Sundays or approximately 320 days per year. Determine the following:

a) Optimal order quantity per order

b) Total annual inventory costs associated with the optimal order size policy

c) Optimal number of orders to place per year

d) Number of operating days between orders, based on the optimal ordering policy

Consider the following alternative: instead of the answer to d), ordering every 12 days. Is this the better alternative? Substantiate your answer.