MM305 UNIT 9 PROJECT Name: Directions: • • • • • In this project you will be using the States Data file that is found in Doc Sharing under the Instructor-Graded Projects: Steps for accessing the States Data file: 1. Open your Excel with PhStat2 2. Click File—Open 3. Select the States Data file Not all questions require the use of technology or the States Date file. You may insert your answers, including any charts, graphs, or output, on this document. Be sure to put your name on this document and save it to your computer. 1. Allen Machines specializes in developing weed-harvesting equipment that is used to clear small lakes of weeds. Allen Machines is contemplating the construction of a machine that would harvest weeds on narrow rivers and waterways. The activities and time in weeks necessary to build one of these experimental machines are shown in the table below. Activity A B C D E F G H Immediate Predecessors none none A A B B C,E D,F Time in Weeks 6 5 3 2 4 6 10 7 1. What is the minimum possible time required for completing the project? 2. What is the latest possible time that Activity D may be started without delaying the completion of the project? 3. What is the latest finish time for Activity F? 4. What is/are the critical path(s)? 2. The following is the activity and associated costs for the renovation of the local high school football stadium. The times are in weeks. Activity A B C D E Immediate Predecessor A B B Time 4 5 3 8 2 Cost ($) 25,000 30,000 15,000 50,000 12,000 1 MM305 UNIT 9 PROJECT F G H C, D C, D E, F 3 7 2 15,000 46,000 20,000 1. What is the critical path for this project? 2. How much of the total budget would be spent in Week 8 (Period 8) with the earliest start budget? 3. Precision Manufacturing has a government contract to produce stainless steel rods for use in military aircraft. Each rod is required to be 20 millimeters in diameter. Each hour, random samples of size n = 4 rods are measured to check process control. Five hours of observations yielded the following: Time 9 A.M. 10 A.M. 11 A.M. Noon 1 P.M. Rod 1 19.8 20.1 19.9 19.7 19.7 Diameter Rod 2 Rod 3 20.4 19.9 20.2 19.9 20.5 20.3 19.8 20.3 20.1 19.9 Rod 4 20.3 19.8 20.1 20.2 19.9 1. Construct the xbar-chart and the R-chart. 2. Is the process in control? 4. Modern Electronics specializes in manufacturing modern electronic components. It also builds the equipment that produces the components. Modern Electronics is considering building a new facility but the estimated profits would be impacted by the type of market that develops. The probability for a strong market is 0.3; for a fair market is 0.5; and for a poor market is 0.2. You are responsible for advising the president of Modern Electronics on the type facility that should be built or to not build a facility at all. The table shows the estimated profits under each market and for each size facility. Build a large facility Build a medium-size facility Build a small facility Do not build a facility Strong Market 550,000 300,000 200,000 0 Estimated Profits Fair Market 110,000 129,000 100,000 0 Poor Market -310,000 -100,000 -32,000 0 1. Provide a recommendation to the president that maximizes profits 2. Provide a second recommendation to the president that minimizes regret. 2 MM305 UNIT 9 PROJECT 5. Consulting income at Kaplan Associates for the period February – July is shown in the table below. Assume that the initial forecast for February is $65,000. Use Exponential smoothing to forecast August’s income. Month February March April May June July Income ($1,000) 70.0 68.5 64.8 71.7 71.3 72.8 1. Use a smoothing constant of α = 0.2. 2. Use a smoothing constant of α = 0.5. 3. Which forecasting constant is best in this situation? 6. Johnson Construction Company is in the process of installing power lines to a large housing development. The company wants to minimize the total length of wire used, which would minimize the company’s cost. The housing development is shown below. Each house has been numbered, and the distances between houses are given in hundreds of feet. 1. What do you recommend to Johnson Construction Company? 3 MM305 UNIT 9 PROJECT 7. The storm drains in the Cedar Rapids, Iowa, have been upgraded following the devastating floods of 2008. The network of storm drains and the capacities are shown below. Determine the maximum flow (in hundreds of gallons of water per minute) from node 1 to node 5. Remember that the arc has both capacity and reverse capacity. From Node 1 2 1 3 1 4 1 5 2 4 3 4 3 5 4 5 To Node Fluid Flow 2 1 3 1 4 1 5 1 4 2 4 3 5 3 5 4 250 100 100 150 400 400 150 200 300 200 250 300 300 250 300 0 8. From the States Data Set the following output for the Income in 2000 and for the Income in 2010 was created. Income 2000 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Income 2010 41773.5 914.6546315 41404.5 #N/A 6467.584924 41829654.74 -0.660527439 0.097844527 25124 29411 54535 2088675 50 Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 50007.02 1063.154673 48818.5 #N/A 7517.638789 56514892.96 -0.456890276 0.498203808 28722 37985 66707 2500351 50 1. Which variable has the greatest relative variation? 4 MM305 UNIT 9 PROJECT 9. You are a consultant working for Kaplan Consulting. The U.S. Department of Labor has requested assistance in evaluating the impact of economic stimulus on the unemployment rate. From the States Data Set the following t test was conducted to answer the question: “Has there been a significant reduction in the national unemployment rate between January and June?” t-Test: Paired Two Sample for Means Jan Unemploy June Unemploy Mean 7.05 6.824 Variance 2.709081633 2.538595918 Observations 50 50 Pearson Correlation 0.955329008 Hypothesized Mean Difference 0 df 49 t Stat 3.282157676 P(T