The purchasing manager (PM) for a steel company must determine a policy for ordering tons of coal to operate eight converters.

Each converter requires exactly five tons of coal per day to operate, and the firm operates 360 days per year.

The PM has determined that the ordering cost is $50 per order, and the cost of holding coal is $3 per ton per year.

(Each order contains the requirement of all converters; therefore, the analysis must consider ‘ordering' and ‘holding' as a system.)

There is a five days' lead time to receive an order of coal. The PM has negotiated a contract to obtained the coal for $12 per ton for the coming year.

a. Determine the optimal quantity of coal to receive in each order.

b. Determine the total inventory-related costs associated with the optimal ordering policy (the result of part a.) per year.