1. The Dulac Box plant produces wooden packing boxes to be used in the local seafood industry. Current operations allow the company to make 500 boxes per day, in two 8-hour shifts (250 boxes per shift). There are 5 full-time workers on each shift. The company has introduced some moderate changes in equipment, and conducted appropriate job training, so that production levels have risen to 300 boxes per shift. Also, with these changes there are now 4 full-time workers on each shift. Labor costs average $10 per hour for each worker on each shift. Capital costs were previously $3,000 per day, and rose to $3,200 per day with the equipment modifications. Energy costs at $400 per day were unchanged by the modifications. The output is measured in terms of the number of boxes that are produced. a) What is the firm's labor hours productivity after the changes? b) What is the percent change in the multifactor productivity before and after the changes? c) Suppose the company now wants to increase productivity as measured by the multifactor productivity factor by 10% at the 300 boxes per shift level of output. To achieve this target, it can only reduce its labor per box. It will use the freed up labor for other activities. How many labor hours per shift will each worker have available for other activities if the company achieves this new level of productivity? 2. Following are the number of victories for the Blue Sox and the hotel occupancy rate for the past eight years. You have been asked to test three forecasting methods to see which method provides a better forecast for the Number of Blue Sox wins. Year Number of Blue Sox Wins Occupancy Rate 1 70 78% 2 67 83 3 75 86 4 87 85 5 87 89 6 91 92 7 89 91 8 85 94 9 87 92 10 88 93 For the following, calculate all forecasts to one decimal place (example, 93.2%) You are asked to forecast the Number of Blue Sox Wins for Year 10. Although you believe there might be a linear regression relationship, your boss has told you to only consider the following three forecasting methods: • 3-period moving average, • 3-period weighted moving average, unfortunately, you spilled coffee on the paper with the weights for each period. You can tell that the weights for the most recent and the second most recent period are 0.6 and 0.3 respectively. The weight for the third most recent period would be consistent with the weighted moving average method we have studied in class. • exponential smoothing with α = 0.35 and the forecast for Year 3 for Number of Blue Sox Wins is 73.0. a) What is the forecast from each of these three methods for Year 11? b) Using one of the forecast evaluation techniques that we have used as part of the homework assignment for this topic and using the forecasts for Years 7 through 10, which forecasting method do you recommend using for preparing your forecast for Year 11? Why? 3. A soft drink maker wants to expand into a neighboring country. They want the product bottled in that country to avoid political issues and to enhance the local image of the product. They have identified two options for the expansion. The first is to build a highly automated plant. The economies of scale would allow them to produce a can of soda for $0.04 and the distribution costs would be $0.02 per can. This facility would cost $1 million per year in fixed costs. The second option would be to build a semi-automated plant that would cost $650,000 per year in fixed costs. However, the cost to produce a can would be $0.07 and the distribution cost would be $0.04 per can. a) Over what range of product would each plant be preferred? b) Suppose the company believes that the demand would be 6,000,000 cans per year. Suppose all costs except the variable cost (sum of the production and distribution costs) for the semi- automated process are certain and can not change. What would the variable cost (the sum of the production and distribution cost) per can for the semi-automated process have to be so that the soft drinker maker is indifferent between the two types of plants? c) Now suppose each alternative has a different capacity. The total estimated demand for the year is 5,300,000 if the company sells each can for $0.32. However, only the highly automated process can produce and distribute this amount. If the semi-automated process is used, the company would only be able to produce and distribute 4,200,000 cans annually. To offset the lower volume, the company will raise the price of each can to $0.35. It will be able to sell all it produces at this price. Using all of the information presented in the problem, which process should it use? Why? 8. Data entry clerks at ARCO key in thousands of insurance records each day. They have just completed a new training program and want to establish a control chart based on the results of this training. Each day random samples of the work of the clerks were collected. The results are shown in the table below. Two hundred records were sampled daily and examined for errors. The number of records with errors was counted. Day Number of Records with Errors Day Number of Records with Errors 1 12 11 12 2 8 12 10 3 4 13 8 4 6 14 10 5 8 15 10 6 8 16 8 7 6 17 10 8 6 18 11 9 2 19 9 10 4 20 8 a) You want to set control limits for the proportion of records with errors. Assume that the past twenty days performance is adequate for establishing the control limits and performing the analysis. Using 95% control limits, what are the upper and lower control limits for the proportion of records with errors? Calculate your proportion defective and the lower and upper control limits to 3 decimal places (0.xxx). Assume that the data provided is sufficient for performing a statistical analysis. b) Plot the control chart and the sample values. c) What would you conclude about the process, in other words, is the process in control? Explain your decision. d) Suppose the industry’s lower and upper control limits are 0.01 and 0.06 respectively. What can this insurance company conclude about its process relative to the industry standards? 9. Sharp Discounts Wholesale Club has two service desks with one server at each desk. There is one desk at each entrance of the store. Customers arrive at each service desk at an average of one every six minutes following a Poisson distribution. The average service time at each service desk is 216 seconds per customer following the exponential service distribution. a) How many customers, on average, are waiting in line for service in front of each service desk? b) How much total time does a customer spend at the service desk either waiting for help or receiving help? c) Looking at only one of the service desks, what is the probability that there are at least two customers already waiting in line waiting for service when the next individual arrives at this service desk? d) Sharp is now considering consolidating its two service desks into one location, staffed by two clerks. The clerks will continue to work at the same individual speed of 216 seconds per customer. • How many customers, on average, are waiting in line? • How much total time does a customer spend at the service desk? e) Do you think the Sharp Discounts Wholesale Club should consolidate the service desks? Explain and your discussion must consider both the economics and the customer service aspects of this waiting line operation. There would be no extra cost for moving the two operations to one operation. The clerks would continue to be paid the same as they were paid at the single desk operation. f) Suppose that it is no longer required that the clerks be paid the same under either operation. Considering the consolidated operation and based on past work experience one clerk is paid $45 per hour and the second clerk is paid $35 per hour. The estimated cost to Sharp for time a customer is at the service desk either waiting or being helped is $0.50 per minute. For the two service desk operation assuming that each clerk will be paid the same hourly rate, what is the maximum hourly rate that each of the clerks can be paid under this two service desk operation so that the total cost of the operation is the same for either arrangement? Assume that there is no cost for consolidating the service. __________________________________________________________________________ CONSTRUCTION TECHNOLOGY 5 __________________________________________________________________________ Climate Assignment Ecologically and climatically appropriate building design. Most traditional construction around the world is well-adapted to its environment and generally makes use of ecologically appropriate building materials and forms. Before mechanical space heating and cooling were available, traditional settlements developed a natural harmony with their climate and had as a consequence, a minimal carbon footprint. With global warming, we are returning to ecologically sustainable and climatically appropriate building designs. Particularly in this assignment, we will be looking at building designs, in climatically diverse locations across Australia and our near neighbours, investigating appropriate solutions for that location from elsewhere in the world that will have a minimum carbon footprint. You will be focusing on traditional solutions (say prior to 1900’s) from around the world, in similar climatic locations; to derive possible solutions for the location you will be assigned. As a group of 5 (minimum) or 7 (maximum) students, you will be allocated a location and your group is to become familiar with its peculiar climatic constraints. You are then to investigate other locations around the world in similar climates and discover the type of traditional building that developed to solve their particular needs for warmth (or cooling) and shelter. The list at the end of this handout has locations from around our region which are climatically diverse. When you have formed your groups a location will be allocated. Please form groups early in the semester. You must research the following topics to determine their influence on building design for your location: 1. The characteristics of the climate. i. Average maximum summer and minimum winter temperatures. ii. Diurnal temperature range both in summer and winter. iii. Humidity levels in summer and winter. iv. Solar characteristics (sun path and intensity of solar radiation). v. Atmospheric conditions (dust, cloudiness, precipitation e.g. mist & rain). vi. Incidence and extent of snow, if applicable. vii. Evaporation rates, rainfall intensities, flooding, fire and any other extremes of climatic conditions encountered at your location. viii. Remember to consider the use of vegetation to control the extremes of the climatic conditions, if at all possible. 2. Lighting needs of the building i. Glare problems; snow or bare ground. ii. Natural and artificial methods of lighting. iii. Lighting control throughout the day. 3. Acoustic background of the building i. External noise levels ii. Internal noise levels The locations chosen have some degree of discomfort in their climate in either summer or winter conditions. It might be the hottest day recorded or length of hot days or the highest evaporation rate. Or it could be the lowest or highest rainfall recorded with associated extremes of flooding or the highest altitude with resultant snow loads. Your group is to overcome these extremities and make your building solution an ecologically sustainable solution using ideas developed from traditional methods sourced from overseas. We are primarily focusing on characteristics of the environment and climate that impinge on building design and deriving solutions that would be acceptable to our culture in Australia. You can use modern building methods or materials to construct your building designs, but the focus is traditional solutions. You can use solar panels to generate both electrical & hot water, but again the focus is traditional solutions. The keywords are ecologically sound solutions that are climatically appropriate to the area you are assigned. Common problems • You are to discover countries that have similar climatic zones, and determine from your research the type of traditional building, that might have appropriate lessons for your allocated area. You must NOT include a general discussion of the cultural, geographic or political background of the country, unless it relates to the design of buildings. Marks will be deducted for padding. • Structural concerns, from snow, floods, earthquake & hurricanes should only be discussed if they affect the lighting, acoustic or thermal characteristics of the building. • You must include a Table of Contents, Conclusion and Reference list (Harvard method); overall it must be a professional report. See the Learning Guide for more details. Assessment (20% of final mark for the unit) Demonstrate how the environmental factors influence the design of traditional buildings in your similar region and how these principles can be applied and implemented to buildings at your location in Australia. This will be done through: 1. A 25 minute maximum verbal presentation (say 15 minute talk {i.e. app. 3 minutes each} and 5 minutes questions to the whole group). The presentation must be accompanied by PowerPoint slides (or similar). 2. A written submission; The length of the report is not critical but there should be input from all members of the group and heat, light and sound should be covered.. Diagrams and photographs are encouraged and should be referenced separately. This is a guide only. You may write a longer or shorter report if you want to do so. It is the quality of what is written that counts. 3. List of Locations: These will be allocated once you form your group Avoca TAS Marree SA Barrow Creek NT Mataranaka NT Birdsville QLD Meekatharra WA Bothwell TAS Menindee NSW Ceduna SA Miena TAS Cobar NSW Moree NSW Coober Pedy SA Peak Hill WA Cromwell NZ Pedirka SA Curie TAS Port Arthur TAS Daly Waters NT Queenstown NZ Derby WA Red Cliffs VIC Emerald QLD Renner Springs NT Halls Creek WA Robinvale VIC Hopetoun VIC Rosebery TAS Innisfail QLD Rotorua NZ Invercargill NZ Taupo NZ Karumba QLD Tumbarumba NSW Laverton WA Wangaratta VIC Mackay QLD Wilpena SA Maningrida NT Windorah QLD 4. Value of the Assignment, including PowerPoint & live presentation: 20% Submission Date: At time of presentation either week 13 or 14, as scheduled later in the semester