Final answer:
Based on the analysis, it would be beneficial for the manager to hire one additional personnel to repair the industrial robots. This would reduce the cost of each repair event and result in long-term cost savings for the company.
Step-by-step explanation:
To determine if the manager should hire any new personnel, let's analyze the situation. A maintenance worker can fix one robot every 8 hours on average, according to an exponential distribution. So, the average time it takes to fix a robot is 8 hours. On the other hand, an average of one robot fails every 3 hours, following a Poisson distribution. This means that on average, a robot is down for 3 hours before it gets fixed.
The cost of each down robot is $100 per hour in lost production. Considering that a worker costs the company $80 per hour in salary, benefits, and equipment, we need to compare the cost of downtime with the cost of additional personnel.
By multiplying the hourly cost of downtime ($100) by the average time a robot is down (3 hours), we find that the cost of each downtime event is $300. Since the average time it takes to fix a robot is 8 hours, the cost of labor for each repair event is $640. Therefore, the total cost for each repair event is $640 + $300 = $940.
Now, let's consider the case of hiring one additional personnel. With an additional worker, the average time it takes to fix a robot would be cut in half, from 8 hours to 4 hours. This would reduce the cost of labor for each repair event to $320. Considering that the cost of one worker is $80 per hour, the additional cost of hiring one worker would be $320 - $240 = $80.
Based on this analysis, it would be beneficial for the manager to hire one additional personnel. This would reduce the cost of each repair event by $60, resulting in long-term cost savings for the company.