# answer the below question managing inventory

**(100 points.***For problems involving the Normal Distribution you can use either Excel functions or the Normal tables provided at the end of the word document attachment.)*

**Question 1 (8 pts)**

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 Appleâ€™s annual inventory turnovers? (4 pts)

b.On average, how many days of inventory did Apple maintain to generate its sales in 2012? (4 pts)

**Question 2 (20 pts)**

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? (5 pts)

b.On a typical day, what is the probability that overtime will be necessary?(5 pts)

c.On a typical day, what is the probability that there will be excess additional police officers? (5 pts)

d.What is the optimal daily number of additional officers that should be hired? (5 pts)

**Question 3 (24 pts).**

A retail outlet sells holiday decorations for $10 per bag.The cost of the product is $8 per bag.Any units not sold during the selling season can be sold for $5 a bag at the end of the season.Assume that demand for these decorations is normally distributed with a mean of 500 and standard deviation of 100 bags.

a. What is the recommended order quantity? (5 pts)

b. What is the probability that at least some customers will ask to purchase the product after the outlet is sold out? (5 pts)

c. Suppose at the end of the selling season, the decorations have no value and have to be disposed of at a cost of $0.10 per bag.Now what is the optimal order quantity? (4 pts)

d. To keep customers happy and coming back, the owner of the store feels that stock-outs should be avoided.What is the your recommended order quantity if the owner is willing to tolerate only a 0.15 probability of a stock-out? (5 pts)

e.Using your answer to part (d) what is the goodwill cost you are assigning to a stock-out? (5 pts)

**Question 4 (24 pts)**

Ray’s Satellite Emporium wishes to determine the best order size for its best-selling satellite dish.Ray has estimated thatweekly demand for this model to be 25 units.His cost to carry one unit is $50 per year and the cost of placing an order with his supplier is $25.He’s open 52 weeks a year.

If Ray were to use the EOQ method,

a. How many dishes should Ray order each time he places an order?

b. What isthe number of times Ray will order this dish each year?

c. How many of this dish will he have on average in inventory?

d. What is the time between one order and the next?

e. What is the annual cost of using the EOQ model for this dish?

f.Ray currently orders in quantities of 50 dishes per order.How much would he save or lose by switching to the EOQ?

(4 pts each)

**Question 5 (24 pts)**

Ray’s Satellite Emporium wishes to determine the best order size for its best-selling satellite dish.Ray has estimated that weekly demand for this model to be 25 units with a standard deviation of 5 units.His cost to carry one unit is $50 per year and the cost of placing an order with his supplier is $25.He’s open 52 weeks a year.Assume weekly demand is normally distributed.

(4 pts each)

- What is Rayâ€™s economic order quantity in this situation? (Hint: Use average annual demand in EOQ formula)
- The lead-time for ordering from this supplier is 3 weeks.What are the mean and standard deviation of demand during lead time?
- Ray desires an in-stock service rate of 95%.How many units should Ray have on-hand at the time he places an order?How many units of safety stock will he carry?
- If Ray increases his in-stock service rate to 99% how many units of safety stock will have to carry?
- Ray is able to negotiate a lead-time of 2 weeks with the supplier.Now what safety stock will he have to carry with 95% and 99% in-stock service levels?
- Suppose Ray is able to reduce the standard deviation of demand (through a combination of lowered prices and loyalty schemes) to 3 units.How will this impact his safety stock assuming lead time of 3 weeks with a service level of 95%?