1.The following table shows financial data (year 2016) for two retailers, Dirt Cheap Wholesale and Kwiki-Mart. Assume that both retailers have an average annual holding cost rate of 20% (i.e. it costs each retailer $2 to hold an item that they procured for $10 for one entire year). Assume that both stores operate 365 days a year.

DIRT CHEAP WHOLESALE KWIKI-MART

Inventories ($MM) 4754 40894

Sales (net $MM) 59217 397206

COGS ($MM) 52762 326606

A) How many days, on average, does a product stay in Dirt Cheap's inventory before it is sold?

B) Both retailers carry a particular brand of a household cleaner, and each retailer incurs $5for acquiring one unit of the household cleaner from the supplier. How much lower (expressed in $'s) is, on average, the inventory holding costfor Dirt Cheap compared to Kwiki-Mart per unit of this household cleaner?

2.Butternut is a ski resort in Massachusetts. One of their triple chair lifts unloads 1296 skiers per hour at the top of the slope. (A triple chair lift can carry three passengers per chair.) The ride from the bottom to the top takes 5 minutes. On average, how many skiersare riding on the lift at any one time?

3. UP Fitness will install 4new "trapezoidal gel-resistance toners" ("trappy" for short), the latest exercise gadget, specifically designed to contour upper back muscles. Clients who want to use these machines arrive at the rate of 85 per hour. The coefficient of variation of the inter-arrival times is 3. If all four machines are busy, UP Fitness clients sign up the waiting list, and use other exercise equipment, waiting for the next available trappy. The trappy experience is intense - on average 150 seconds of explosive exercise intensity. The standard deviation of the usage times is quite small - only 30 seconds.

A) What is the service rate of each trappy machine?

B) What is the utilization of each trappy machine?

C) On average, how many UP Fitness clients are using a trappy?

D) On average, how long does a UP Fitness client need to wait before using a trappy? E) On average, how many UP Fitness clients are in the system (i.e., waiting in line or using a trappy)?

4. Precision Parts.Berkeley Manufacturing Company (BMC) employs a four-step production process to produce metal-alloy-coated precision parts. The first step is fabrication. The fabrication machine takes 7.5 minutes per unit to mold raw material into the proper shape of a part. The second step is coating. The coating machine applies a layer of one of many metal alloys at high heat. The coating machine takes 24 minutes, and it can coat up to six units of parts (of the same metal alloy) at a time. The third step is cooling. It takes 50 minutes for a coated part to cool. No equipment is required for this step, and there is plenty of cooling space. The fourth step is polishing, which takes 5 minutes per part. For simplicity, you should assume the production system operates continuously (i.e., 24 hours a day) and that the system has been running for some time.

A) Currently, BMC is following a production sequence in which each part produced is a coated with a different alloy than the last one (e.g., an aluminum-alloy part is followed by a titanium-alloy part, which is followed by abronze-alloy part, etc.). As a result, the coating machine can coat one unit at a time. What is the capacity of the production process?

B) In February, BMC purchased an additional polishing machine. What is the capacity of the production process now? Explain why it has (or has not) changed from your answer to Question A.

C) In March, BMC changed to produce parts in batches of two (e.g., produce two aluminum-alloy parts, followed by two titanium-alloy parts, which is followed by two bronze-alloy parts, etc.). What is the capacity of the production process now (assume no setup time for each batch)? Explain why it has (or has not) changed from your answer to Question B.

D) In April, BMC purchased a second coating machine. (BMC continues to produce parts in batches of two.) What is the capacity of the production process now? Explain why it has (or has not) changed from your answer to Question C.

E) In April, BMC installed fans throughout the cooling space which reduced the cooling time to 15 minutes. What is the capacity of the production process now? Explain why it has (or has not) changed from your answer to Question D.

5. One of the top-selling items at a gift shop at Hilo, HI are autographed pictures of Jack Star. Sales are 18 pictures per week, and the supplier charges $60 per picture. Currently the gift shop orders a 6-week supply at one time from the supplier. The total cost of placing each order is $45. Annual holding costs are $15 per picture. Assume that the shop operates 52 weeks/year.

A) What is the shop's current average inventory level?

B) What is the shop's current annual inventory holding cost?

C) What is the shop's current annual ordering cost (total cost of placing orders over the entire year)?

D) Compute current total annual costof ordering and carrying inventory.

E) If the shop wishes to minimize total annual cost, what size orders should be placed?

6.Handi Inc., a maker of cellphones, procures a standard display from LCD Inc. via an options contract. At the start of quarter 1 (Q1) Handi pays LCD $3.5 per option. At that time Handi's forecast of demand in Q2 is Normally distributed with mean 24000 and standard deviation 6000. At the start of Q2 Handi learns exact demand for Q2 and then exercises options at a fee of $4.5 per option (for every exercised option LCD delivers one display to Handi). Assume Handi starts Q2 with no display inventory and displays owned at the end of Q2 are worthless. Should Handi's demand in Q2 be larger than the number of options held, Handi purchases additional displays on the spot market at $12 per unit.

For example, suppose Handi purchases 30000 options at the start of Q1 but at the start of Q2 Handi realizes that demand is 35000 units. Then Handi exercises all of its options and purchases 5000 additional units on the spot market. If, on the other hand, Handi realized demand is 27000 units, then Handi only exercises 27000 options.

A) If Handi chooses to purchase 28,000 options, what is the probability that Handi needs to purchase displays from the spot market?

B) If Handi wants to maximize the profit, how many options should Handi purchase from LCD? C) Suppose the price for the display on the spot market price changes to $8 per unit, how many options should Handi purchase from LCD to maximize the profit?