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 holding a bill in inventory costs 10 percent of its value annually.She knows that each order for these bills costs $300 for clerical and armoured car delivery costs,and that order lead time is six days. Assuming a thirty-day month,if she were to order 6,000 bills at a time,what would be the length of an order cycle?
A)0.48 days
B)2.08 days
C)6 days
D)8.4 days
E)14.4 days

Question

Quizplus · Accepted Answer

First, we need to calculate the Economic Order Quantity (EOQ):

EOQ = sqrt[(2DS)/(H)]
where D = demand per month (12,500 bills), 
S = ordering cost ($300 per order), 
and H = holding cost (10% of $100 per bill per year = $10 per bill per year, or $0.83 per bill per month)

EOQ = sqrt[(2 x 12,500 x 300)/0.83] = 20,970

So the operations manager should order 20,970 bills at a time to minimize the total cost of ordering and holding inventory.

Next, we can calculate the length of an order cycle:

Order cycle = EOQ / D
Order cycle = 20,970 / 12,500 = 1.68 months

However, the question asks us to give the answer in days, so we need to convert months to days:

Order cycle = 1.68 months x 30 days/month = 50.4 days

Finally, since the question asks for the length of an order cycle if the manager orders 6,000 bills at a time, we need to adjust our answer:

Order cycle = (6,000 / 12,500) x 50.4 days = 24.19 days

Rounding to the nearest tenth, we get:

Order cycle = 24.2 days

Therefore, the correct answer is E) 14.4 days.

The Operations Manager for Shadyside Savings & Loan Orders Cash