This is the Atlas Inc problem from the process analysis module practice questions. Atlas Inc is a toy manufacturer with seven work stations and five workers. Worker one is responsible for steps one and two, and it takes worker one 50 seconds per unit. Worker two is responsible for steps three and four, which takes worker two 60 seconds per unit. The remaining workers are allocated one per step, so worker three is responsible for step five, which takes 30 seconds. Worker four is responsible for step six, which takes 45 seconds. And worker five is responsible for step seven, and that step takes 40 seconds. The first question asks us about the bottleneck. Recall the bottleneck is the resource with the smallest capacity. Let's consider each worker's capacity. Worker one has a capacity of 1 unit per 50 seconds. Multiplying this by 60 seconds per minute gives us 1.2 units per minute for worker one. Worker two has a capacity of 1 unit per 60 seconds. Times 60 seconds per minute gives us 1 unit per minute. Worker three has a capacity of 1 unit per 30 seconds, again, times 60 seconds per minute, gives us 2 units per minute,. Worker four has a capacity of 1 unit per 45 seconds, times 60 seconds per minute gives us 1.33 units per minute for worker four. And worker five has the capacity of 1 unit per 40 seconds times 60 seconds per minute, gives us 1.5 units per minute. Now if we compare all of these capacities, we see that worker two has the smallest number, with 1 unit per minute. So the bottleneck is worker two. The second question asks us what the capacity of the assembly line is. So far we've been working in units per minute, but in this case the question specifies that this is finished units per hour. Now recall that the process capacity is the minimum of the capacity of all of the resources. This is the minimum of the capacity of worker one, of worker two, up through worker five. We know from the previous question that the smallest capacity is the capacity of worker two. And we found that this was one unit per minute. Simply multiplying this by 60 minutes per hour, Gives us 60 units per hour. So the answer to question two is simply 60 units per hour. The third question asks us about the utilization of worker four, ignoring the first and last units. Recall that utilization equals flow rate over capacity. Flow rate is simply 1 unit per minute, which we found earlier, and the capacity of this particular resource is 1.33 units per minute. Now all we have to do is substitute these numbers into the equation and solve. So we have 1 unit per minute over 1.33 units per minute and this is simply equal to 0.75. The fourth question asks us about the average labor utilization of the workers, again ignoring the production of the first and last units. Recall that average labor utilization equals labor content divided by labor content plus idle time. Let's look at labor content by worker. Worker one spends 50 seconds on each unit, worker two spends 60 seconds per unit, worker three spends 30 seconds, worker four spends 45 seconds, worker five spends 40 seconds. And adding all of this up gives us 225 seconds of labor per unit. Now for idle time, because the process capacity is 1 unit per 60 seconds, worker one is idle for 60- 50 seconds, which equals 10 seconds. Worker two is idle for 0 seconds, 60- 60. Worker three is idle for 30 seconds, worker four for 15 seconds and worker five for 20 seconds. Summing this up gives us 75 seconds. Then we can just substitute this into our equation above. So we have that average labor utilization, Equals 225 seconds divided by 225 seconds, plus 75 seconds. And 225 over 300 = 0.75. Finally, the last question asks about the cost of direct labor. The definition of this is total wages per unit time over flow rate per unit time. Where unit time is hour. Now, total wages per hour is given by $15 per hour, per worker, times 5 workers. And this equals $75 per hour. Now, the flow rate per hour is 1 unit per minute, from earlier, times 60 minutes per hour, Which is simply 60 units per hour. And then our direct labor costs, Are $75 per hour divided by 60 units per hour, and that simplifies to $1.25 per unit.
