8.1. Dulles Electric Company buys 1 million tons of coal annually to burn at its power plant. The company wants to invest in a unit train that will haul coal from the mine to the power house, where it is dumped in a large field. The shipping cost is expected to be $40 a ton. The cost of capital to Dulles is 10% per annum. The price of coal is $180 a ton. The cost of processing an order is $12,500. Find the optimal capacity of the unit train. How often does it make the trip to the mine?

33,710 tons, Approximately every 12 days

8.2. Hull Baking Company uses 250,000 lb of sugar annually in its cakes and pastries. The company can order the sugar in 100 lb bags, at the cost of $19.50 per bag, delivered. The cost of preparing and sending an order is $50. The storage and handling costs amount to $2 per bag per year, based on average inventory. The cost of capital for Hull is 12%. Calculate the optimal size of an order.

240 bags

8.3. Rusk Corporation sells 185,000 gallons of paint annually at several retail outlets. The ordering cost per order is $75, and its cost of capital is 10%. The storage and handling cost for paint is $2 per year, based on average inventory. Rusk buys the paint from the manufacturer according to the following price schedule: 1 - 999 gallons at $11 per gallon, 1000 - 9999 gallons at $10 per gallon, and 10,000 gallons and over at $9 per gallon.

(A) Find the optimal order quantity for Rusk. 10,000 gallons

(B) For this optimal order size, what is the total annual cost of paint? $1,680,888

(C) What is the annual cost of the inventory system? $15,888

8.4. Seward Company buys 35,000 lb of flour annually. The cost of placing an order is estimated to be $35, and its cost of capital is 12%. The storage and handling costs are estimated to be 2 cents per lb annually, at the average inventory level. The price of flour is as follows: up to a 1000 lbs at 12 per lb, 1,000 to 4999 lbs at 11 per lb, and 5,000 lbs and over at 10 per lb. Find the optimal order quantity of flour for Seward.

8750 lb