The following represents a project that should be scheduled using CPM: (a) Using the PERT method, find the critical path. (b) What is the expected project completion time? The desired daily output for an assembly line is 400 units. This assembly line will operate 480 minutes per day. The following table contains information on this product's task times and precedence relationships: (a) What is the required workstation cycle time to meet the desired output rate? (b) Balance this line using the largest number of the following tasks. Use the longest task time as a secondary criterion. (c) What is the efficiency of your line balance, assuming it is running at the cycle time in part (b)? (You should show your work for full credit. Round your answers to two decimal points.) A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of 3.0 per minute. In serving themselves, customers take about 30 seconds, exponentially distributed. (a) How long would you expect it to take to get a cup of coffee? (b) If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 22 seconds, how long would you expect it to take (in minutes) to get a cup of coffee, including waiting time? A project to build a new bridge seems to be going smoothly. A major milestone has been reached where the first two activities have been totally completed and the third activity is 53% complete. The planners were expecting to be only 45% through the third activity at this time. The first activity involves prepping the site for the bridge. It was expected that this would cost $1,200,000 and it was done for $1,310,000. The second activity was the pouring of concrete for the bridge. This was expected to cost $9,600,000 but was actually done for $8,000,000. The third and final activity is the actual construction of the bridge superstructure. This was expected to cost a total of $8,500,000. To date, they have spent $3,200,000 on the superstructure. Calculate the schedule variance, cost performance index for the project to date. (You should show your work for full credit. Round your answers to two decimal points.)