The purchasing manager for the Atlantic Steel Company must determine a policy for ordering coal to operate 12 converters. Each converter requires exactly 5 tons of coal per day to operate and the firm operates 360 days per year. The purchasing manager has determined that the ordering cost is $80 per order and the cost of holding coal is $2.40 per ton per year. The purchasing manager has negotiated a contract to purchase the coal for $12 per ton for the coming year.
a. Determine the optimal quantity of coal to purchase for each order.
b. Determine the total inventory-­?related costs associated with the optimal ordering policy (do not include the cost of the coal).
c. If 5 days of lead time are required to receive an order of coal, how much coal should be on hand when an order is placed?