Question

Question 1

In fiscal year 2012, Apple Inc. (NASDAQ: AAPL) reported a cost of goods sold of $87,846 million and inventory valued at $2,583 million.

a. What are Apple’s annual inventory turnovers?

b. On average, how many days of inventory did Apple maintain to generate its sales in 2012?

Question 2

The Bridgeport City Police need assistance in determining the number of additional police officers needed to cover daily absences due to injuries, sickness, vacations, and personal leave. Records indicate that the daily demand for additional police officers is normally distributed with a mean of 50 officers and a standard deviation of 10 officers. The cost of an additional police officer is based on the average pay rate of $150 per day. If the daily demand for police officers exceeds the number of additional officers available, the excess demand will be covered by overtime at the pay rate of $240 per day for each overtime officer.

a. If the number of additional police officers available is greater than demand, the additional officers will have to be paid anyway. If the number of officers is less than demand, overtime will have to used and paid for. What are Cu and Co in this instance?

b. On a typical day, what is the probability that overtime will be necessary?  

c. On a typical day, what is the probability that there will be excess additional police officers?

d. What is the optimal daily number of additional officers that should be hired?

Answer 1

Answer 1) Apple's annual inventory turnovers is

Cost of goods sold/inventory valued, which is nothing but,

87,846 / 2,583 = 34.009291

Rounded value = 34, So Apple's annual inventory turnover ratio = 34

Answer 2) Total number of days in a year / inventory turnover ratio

With the help of above formula, we can calculate the total number days of inventory that Apple needs to generate in 2012.

Total number of days in 2012 = 365

Inventory ratio = 34 (calculated in above answer)

= 365/34 = 10.7352, rounded = 11. So Apple needs to keep 11 days of inventory.