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. How often should the credit union replenish the ATM, that is, what is the elapsed time between each refill?

Select one:

A. 3.6 weeks

B. 1.8 weeks

C. 1.0 week

D. 2.0 weeks

Explanation / Answer

D=Average Annual cash withdrawal= 40*200*52=416000   (taken 52 weeks / year)

H=Holding Cost=0.1

Ordering Cost=O=100

therefore EOQ= Sqrt(2*D*O/H)= sqrt(2*416000*100/0.1)=28844.41

hence turns= 416000/28844.41=14.42

therefore replenishment should be every =52/14.42=3.6 weeks

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