This is the Assign Tasks to Workers problem from the Productivity Module practice problems. In this problem, we are looking at a conveyor paced line with six tasks distributed among four workers. Currently, worker 1 performs task 1, which takes 30 seconds. Worker 2 performs task 2, which takes 25 seconds. Worker 3 performs tasks 3 and 4, which take 75 seconds total. Finally, worker 4 performs tasks 5 and 6, which take 45 seconds total. The first question asks us for the capacity of the current conveyor paced line. Recall that the capacity of the current line is given by the capacity of the bottleneck, where the bottleneck is the resource with the lowest capacity. With the current setup, the capacity of worker 1 is 1 unit per 30 seconds. To convert this into units per hour, note that there are 3600 seconds per hour. So 1 over 30 units per second times 3600 seconds per hour is 120 units per hour. Similarly, the capacity of worker 2 is 1 unit per 25 seconds, or 144 units per hour. The capacity of worker 3 is 1 unit per 75 seconds, or 48 units per hour. And finally, the capacity of worker 4 is 1 unit per 45 seconds, or 80 units per hour. The bottleneck is worker 3, with a capacity of 48 units per hour. Therefore, the capacity of the current line is also 48 units per hour. Now in problem 2, we can reallocate the tasks to maximize the capacity, subject to a couple of constraints. A worker can perform at most two adjacent operations, and the tasks are done in numerical order. We have the task and the total time for each task listed in the first two columns. Let's see how we can group these tasks to maximize the line capacity. For our first guess, let's group tasks 1 and 2 together, so worker 1 will spend 55 seconds on his tasks. If we group tasks 3 and 4, worker 2 would spend 75 seconds on his tasks. This exceeds the time of 55 seconds for worker 1, so grouping these tasks would decrease the process capacity. Let's leave them separate. So, worker 2 performs just task 3, which takes 35 seconds. Now we can group tasks 4 and 5 together because they sum to 55 seconds. So, worker 3 spends 55 seconds, and worker 4 spends 30 seconds. Alternately, we could assign just task 4 to worker 3 and group tasks 5 and 6 together. In both of these cases, the slowest resources would have a capacity of 1 unit per 55 seconds. Thus, the process capacity for these allocations is 1 unit per 55 seconds, or 65.5 units per hour. Can we do any better? Well, if we try to group tasks 2 and 3 together, then that worker would take 60 seconds per unit, which is slower than the previous scenario. If we group tasks 3 and 4 together, then we have the original scenario, and that worker would take 75 seconds per unit. Since workers can only perform at most two tasks, then we cannot do any better than 1 unit per 55 seconds, or 65.5 units per hour. Now for question 3. Suppose we don't have the restriction about order imposed in the previous problem. Can we do any better? Again, we want to make educated guesses and see if we can improve the capacity. We see that the two highest task times are 35 and 40 seconds. So let's assign worker 1 to just task 3 and worker 2 to task 4. Then we are left with four tasks. However, the best we can do is assign tasks 1 and 2 to worker 3 for a total time of 55 seconds, and tasks 5 and 6 to worker 4 for a total time of 45 seconds. This is no better than the allocation we found in question two. What if instead, we assign task 4 to worker 1, and tasks 3 and 5 to worker 2, for a total time of 50 seconds? Then we are left with task 1 at 30 seconds, task 2 at 25 seconds, and task 6 at 30 seconds. Again, the best we can do is to combine two of these tasks for a total time of 55 seconds. Thus, even though we have less constraints in this question, the best we can do is still 1 unit per 55 seconds, or 65.5 units per hour. For questions 4 and 5, we now factor in demand, which is 50 units per hour. Question 4 asks us for the takt time. Recall that the takt time is the speed at which the line must produce in order to keep up with demand. In order to keep up with demand, the line can spend 1 hour per 50 units, which is 3600 seconds per unit, or 72 seconds per unit. Finally, question 5 asks us for the target manpower. Recall this is simply labor content divided by takt time. Labor content is the sum of time to complete all 6 tasks, which is 175 seconds. And from above, takt time is 72 seconds. 175 divided by 72 is 2.43. Rounding up, this means we need three workers.