A university credit union that serves a very large student population has an ATM

Question

A university credit union that serves a very large student population has an ATM in the student union where several cafes, restaurants, game rooms, gift shops and other unique shops are located. The average cash withdrawal at the ATM is about $40. Average number of cash withdrawals per week is about 200. The credit union estimates that the fixed cost of filling the ATM Is about $100 regardless of the amount of cash in. Annual cost of money is 10% per year. Assume 52 weeks in a year. If the credit union expects the demand for cash to triple next year, how much should the credit union keep at the ATM. that is, what is the new optimal quantity (inventory level, Q)? Select one: $86,532 $37,497 $49,959 $416,000

Explanation / Answer

Annual Demand (200 withdrawls * $40 * 52 weeks * 3times increase) $ 1,248,000.00 Filling Cost $              100.00 Cost of Money 10% Optimal Quantity = 2AF/C where A = Annual Demand F = Filling Cost C = Cost of Money Optimal Quantity = 2AF/C = (2 * 1248000 * 100) / 10% = $49959.98 units Hence, the correct answer is option C - $49,959

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