Question

Central University uses $123,000 of a particular toner cartridge for laser printers in the student computer labs each year. The purchasing director of the university estimates the ordering cost at $45 and thinks that the university can hold this type of inventory at an annual storage cost of 0.83 of the purchase price. The purchase price of each cartridge is $4.00/unit.   How many times per year should the purchasing director place an order to minimize the total annual cost of purchasing and carrying?

*to two decimal places

Answer 1

Given: Annual $ usage = $123,000

Price per cartridge = $4

Annual Demand = D = Annual $ usage / Price per cartridge = $123,000 / $4 = 30,750 units

Ordering cost = S = $45

Annual Storage Cost = H = 0.83 of purchase price = 0.83 * 4 = $3.32‬

To minimize the total annual cost of purchasing and carrying, we have to place an order for economic Order quantity

Economic Order Quantity EOQ = = = 913.008 = 913.01 units

No. of orders per year = D / EOQ = 30750 / 913.01 = 28.39 = 33.68 times

Hence, the purchasing director should place the order 33.68 times a year to minimize total purchasing and carrying costs.

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