Hi, I need help with the following question and I\'m looking for the explanation

Question

Hi, I need help with the following question and I'm looking for the explanation. Thanks!

The purchasing manager for the Pacific 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 20% of the average dollar value of inventory held. The purchasing manager has negotiated a contract to obtain 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 (do not include the cost of the coal).
c. If five days' lead time is required to receive an order of coal, how much coal should be on hand when an order is placed?

Explanation / Answer

Annual Demand of the coal = 360 x 5 x 12 = 21,600 tons of coal

a. Optimal order quantity = (2AO/C)1/2 where A = Annual Demand, O = Ordering Cost and C = Carrying Cost
Carrying Cost = 12 x 20% = $2.4 per ton
Optimal order quantity = (2 x 21,600 x 80 / 2.4)1/2 = 1,200 tons

b. Total Inventory Cost at Optimal Order Quantity = Ordering Cost + Carrying Cost
Ordering Cost = (21,600 / 1,200) x 80 = $1,440
Carrying Cost = (1,200 / 2) x 2.4 = $1,440
Total Inventory Cost at Optimal Order Quantity = 1,440 + 1,440 = $2,880

Note: At optimal order quantity Ordering cost is always equal to Carrying Cost.

c. Average Daily usage = 12 x 5 = 60 tons
Re-order Level = Average Consumption per day x Lead time = 60 x 5 = $300 tons
Thus, 300 tons of stock should be in hand when an order is placed.

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