Airphone, Inc., manufactures cellular telephones at a processing cost of $47 per unit. The company produces an average of 250 phones per week although there are 16% defective phones. Each phone takes one hour to make. At this time, none of the defective phones can be reworked but can be sold as is. Each good phone is sold for $125. The defective phones are sold for parts that provide $12 in revenue per phone.

The output is defined as the revenue that the company receives.

- a) What is the company’s labor hours productivity and what is its multifactor productivity?

- b) Suppose that the company is now able to rework half of the defective phones. It takes an additional 0.5 hours to rework a defective phone. The cost of reworking a defective phone is $16. After it has started reworking the defective phones that can be reworked, what is the company’s labor hours productivity and what is its multifactor productivity? The remaining defective phones that cannot be reworked can still be sold for parts that provides $12 in revenue per phone.

- c) What is the percent change in the multifactor productivity if the initial process used is the one without the rework capability and is then replaced by the process with the rework capability?

** **2. (18 points)

Doug Moodie is the president of Garden Products Limited. Over the last 5 years, his vice president of marketing has been providing the sales forecast using his special forecasting technique. The actual sales for the past ten years and the forecasts from the vice president of marketing are given below.

Year |
Sales |
VP/Marketing Forecast |

1 | 170,300 | — |

2 | 168,250 | — |

3 | 165,700 | — |

4 | 169,000 | — |

5 | 168,000 | — |

6 | 167,300 | 170,000 |

7 | 175,250 | 170,000 |

8 | 172,500 | 180,000 |

9 | 156,700 | 180,000 |

10 | 176,300 | 160,000 |

Doug wonders if perhaps a weighted moving average or an exponential smoothing approach to forecasting might be better than having the vice president of marketing prepare the forecast. Doug wants to evaluate a three-period weighted moving average with weights of 0.30 and 0.15 for the second most recent and third most recent periods and the remaining weight(s) consistent with how we have used this method this term. He also wants to evaluate the exponential smoothing with an α = 0.30 and a starting forecast for period 4 of 170,000 units.* *

- a) Which of the three methods (weighted moving average, exponential smoothing and VP/Marketing) provides the best forecasting method if you were to evaluate these methods based on their forecasting accuracy for Years 6 through 10. Use one of the evaluation methods we have discussed.

- b) What would be the forecast for Year 11 using both the weighted moving average and the exponential smoothing methods?
- (24 points)

Merrimac Manufacturing has always purchased a certain component part from a supplier on the East Coast for $50 per part. The supplier is reliable and has maintained the same price structure for years. Recent improvements in operations and reduced product demand have cleared up some capacity in Merrimac’s own plant for producing component parts. The particular part in question can be produced internally by Merrimac at $20 per part, with an annual fixed investment of $27,000.

a) Over what range (quantity) of product would each of the two options be the preferred one?

b) As an alternative, a new supplier located nearby is offering to produce parts on the following cost schedule. For the first 100 parts, the cost is $52 per part. For each part in excess of 100, the cost per unit drops to $46 per part. Considering just the two suppliers, over what range (quantity) of product would each supplier be the preferred one?c) The company is now considering only these two options: the new supplier with the cost information provided in part b) and producing it internally. Considering these two options, over what range (quantity) of product would each option be the preferred one?

- (31 points)

The Older Then Dirt potting soil company uses a machine to fill 500-ounce bags of enriched potting soil. The industry group has set limits on what can be called a 500-ounce bag: a 500-ounce bag of dirt must weigh at least 486 ounces and not more than 514 ounces. The company wants to operate its process at a minimum process capability of 1.10.

a) The specification limits have not changed. Suppose that the mean of the process is now 502 ounces with a standard deviation (σ) of 2 ounces. What is the range (upper and lower limits) on the mean of the process to maintain a C_{pk} of 1.10 or greater?

b) Suppose that the company is now operating the process with a mean of 504 ounces and a standard deviation (σ) of 4 ounces. Is the company currently capable of meeting the industry group’s specification standards if the company’s minimum C_{pk} is 1.10? If it is not, explain if it is due to a drifting of the mean or too much variability. Explain

c) Now suppose that the company is operating the process with a mean of 497 and continues to use a process capability of 1.10 or greater. What is the maximum acceptable value of the standard deviation (σ) to ensure that the process capability is at least 1.10?d) Suppose that the company can maintain an average weight of 504 ounces and a standard deviation (σ) of 4 ounces. The company does not believe it can improve on these values. The company wants to see if the industry group would be willing to adjust its spec limits rather than keep them at 486 and 514 so that Older then Dirt can meet the minimum C_{pk} of 1.10. What should the company tell the industry group that the spec limits need to be to achieve a C_{pk} of 1.10 or greater? Why?

6 (16 points)

A toy company has developed a new toy for the upcoming Christmas season. Since this toy is considerably different from the ones it has manufactured previously, the company will need to develop a new production facility for it. Three facility sizes – small, medium and large – are under consideration. Given the nature of the toy market, the company is unsure as to what demand level it will encounter. The preliminary analysis is to be based on the demand being low, average, or high. The accompanying table shows the estimated profits, in $1,000’s, of the various facility-size demand combinations. These estimated profit amounts factor in the cost of the operation as well as the time value of money.

Demand Level

Facility Size | Low | Average | High |

Small | $750 | $900 | $900 |

Medium | $350 | $1,100 | $1,300 |

Large | -$250 | $1,000 | $4,000 |

The company’s initial assessment of the probabilities of the different market sizes is:

- probability of low = 0.5
- probability of average = 0.3
- probability of high = 0.2

a) Draw the decision tree that would help in this analysis. Be sure to indicate all probabilities and payoffs.

b) Based on an expected value analysis, what is your recommendation for the facility size that the company should select? Why?

c) Now, consider only the large and medium facility sizes. Keeping all other variables and values the same as in the problem, what would the profit for the medium facility under the Low Demand scenario need to be so that the expected profit of these two options (small and medium) are equal?

7 (14 points)

A medical clinic is considering 3 sites for the location of its new clinic. It has collected the following information. The scores for the non-financial data are on a 0-3 scale with three being best. It is possible to score a 3.0 for any of the factors.

Factor |
Factor Weight |
Downtown |
Midtown |
Suburb |

Building Cost | 0.30 | $5 million | $6 million | $4.5 million |

Road Access | 0.25 | 1.5 | 3.0 | 2.4 |

Bus Access | 0.20 | 3.0 | 1.8 | 1.2 |

Safety | 0.20 | 1.8 | 2.4 | 3.0 |

Site Size | 0.05 | 2.4 | 1.2 | 2.4 |

a) Using the factor scoring (factor rating) approach as we studied in class, which site do you recommend? Why?

b) Suppose that the clinic wants to add another factor, Profit, to its analysis. This factor would be assigned a weight of 0.20 by reducing the Road Access factor weight to 0.05. The values of the Profit for each site are as follows:

Site A: $6.0 million Site B: $4.0 million Site C: 3.0 million

Using the factor scoring (factor rating) method with this additional information, which site is now recommended? Why?

- (18 points)

The Farr-Kroger Classic is a women’s professional golf tournament played each year in Ohio. Listed below are the total purse winnings (the amount of money that is distributed to the top golfers) and the prize for the winner for the 15 years from 1999 through 2013. The operators of this golf tournament believe that there is a relationship between the purse winnings and the prize. There is also a belief that both of these are increasing over time.

Year |
Purse Winnings |
Prize |

1999 | $225,000 | $33,750 |

2000 | $275,000 | $41,250 |

2001 | $325,000 | $41,250 |

2002 | $325,000 | $48,750 |

2003 | $350,000 | $52,500 |

2004 | $400,000 | $60,000 |

2005 | $450,000 | $67,500 |

2006 | $500,000 | $75,000 |

2007 | $500,000 | $75,000 |

2008 | $575,000 | $86,250 |

2009 | $700,000 | $105,000 |

2010 | $800,000 | $120,000 |

2011 | $800,000 | $120,000 |

2012 | $1,000,000 | $150,000 |

2013 | $1,000,000 | $150,000 |

In answering these questions, you must use the correct independent and dependent variables.

a) Suppose that the prize is a function only of time. Using linear regression, develop a projection for the amount of the prize for the winner for the year 2016 based on the information you have provided through this part of the problem. Identify the independent and dependent variables you are using considering the problem statement.

b) Using linear regression, develop a projection for the amount of the prize for the winner for the year 2016 based only on the relationship between the prize and the purse winnings. From the $1,000,000 Purse Winnings in 2013 the Classic tournament committee has and will continue to increase the purse winnings $25,000 per year for the next five years. Identify the independent and dependent variables you are using considering the problem statement.

c) Would you use either of the methods from a) or b) to project the prize for the winner for 2016? Explain your answer, including the key factors that we studied that should be considered in making this decision.

9 (19 points)

The Fred and Barney Cookie Co. has decided to implement statistical quality control to its chocolate chip cookie baking line. The company is concerned that it has been providing too many burned cookies. Two times per day over the last 5 days, the company has taken samples of 250 cookies and counted the number of burned cookies in each sample. A burned cookie is considered a defective cookie. The results are shown below. The company wants to use a percent defective control chart using 3σ control limits. Assume that the data provided is sufficient for preparing the appropriate control charts.

Sample |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Number of Burned Cookies |
5 | 5 | 4 | 6 | 2 | 4 | 6 | 5 | 6 | 7 |

a) What are the upper and lower control limits? Calculate your results to 3 decimal places (0.xxx).

b) Plot the control chart including the centerline, the UCL the LCL, and the sample values.

c) What would you conclude about the chocolate chip cooking baking line using the percent defective burned cookies as a measure? Explain your decision.

d) Suppose Fred and Barney subscribes to a cookie industry magazine that states that the standard for burned cookies is 2.0% to 6.5%. Comment on Fred and Barney’s process compared to the industry standards looking at the individual sample values.

** **

- (29 points)

Benny the Barber owns a barber shop with two-chairs (stations for two barbers). However, he is the only barber working there at this time. His customers are arriving at the rate of one every thirty minutes. The arrival rate distribution follows a Poisson distribution as Benny does not take appointments. On average, it takes Benny an average of 24 minutes to give a haircut and this service time follows an exponential distribution. Using this information, answer the following questions.

a) The average number of customers waiting for a haircut.

b) The average time a customer is in the shop.c) Suppose Benny’s waiting area has only three chairs for waiting customers. What percent of the time will a customer arriving not be able to find a chair to sit in?

d) Benny is concerned about losing revenue and is considering adding another barber. He believes that for every hour a customer is in his shop either waiting for a haircut or having his haircut he loses $3 of revenue. If he hires the barber, he will pay him a salary of $10 per hour. Benny currently pays himself $15 for cutting hair. Answer the following questions for the two-chair operation. Assume that the arrival rate will not change and that the second barber will work at the same pace as Benny. Customers cannot ask for a specific barber but will take the first one available.

Based on the cost of the operation and using the information provided here, which operation (Benny or Benny combined with the second barber) would be the most cost effective? Provide the cost of operation of each scenario. Base your cost analysis only on the information provided here and ignore the time value of money.

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