# Optimal Order Quantity in Production

Problem 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?

Problem 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.

Problem 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.

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

Problem 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.

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#### Solution Summary

The solutions to given problems explain step by step methodology to estimate the optimal order quantity and various inventory costs.