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, games 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. How often should the credit union replenish the ATM, that is, what K the elapsed time between each refill? Select one: 3.6 weeks 1.8 weeks 1.0 week 2.0 weeks

Explanation / Answer

Annual Demand (200 withdrawls * $40 * 52 weeks) $      416,000.00 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 * 416000 * 100) / 10% = $28844.41 No of orders = Annual Demand/Optimal Quantity = 416000/28844.41 = 14.42 Elapsed Time Between Orders = 52 weeks / No of orders = 52/14.42 = 3.6055 Hence the correct answer is Option A - 3.60 weeks

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