The Operations Manager for Shadyside Savings & Loan orders cash from her home office for her very popular "BIG BUCKS" automated teller machine, which only dispenses $100 bills. She estimates that this machine dispenses an average of 12,500 bills per month, and that carrying a bill in inventory costs 10 percent of its value annually. She knows that each order for these bills costs $300 for clerical and armored car delivery costs, and that order lead time is six days. Assuming a 30-day month, what is the economic order quantity?

3,000 $100 bills equivalent to $300,000

Explanation:

The economic order quantity (EOQ) is the optimum quantity of a good to be purchased or required at a time in order to minimize ordering and carrying costs in inventory.

EOQ = the square root of [ (2 times the annual demand in units times the incremental cost to process an order) divided by (the incremental annual cost to carry one unit in inventory) ]

annual demand in units = 12,500 x 12 = 150,000 incremental costs to process an order = $300 incremental annual cost to carry one unit in inventory = 10% x 100 = $10

EOQ = √[ (2 x 150,000 x $300) / $10] = √ ($90,000,000 / $10) = √9,000,000 = 3,000 bills