To keep your production plant up and running, you are constantly looking for new employ- ees. Understanding the abilities of an applicant is not easy. By conducting an interview with an applicant, your HR department can estimate the applicant's abilities which will provide you with the information required to make the right hiring decisions. Within your company, there are four employees working at the HR department who are responsible for conducting these interviews. Each employee is able to conduct four inter- views every three hours on average, the length of these interviews follows an exponential distribution. Interviews are not scheduled, so applicants can come for an interview at any time. For question 1 & 2, assume there are 12 applicants arriving per 3 hours on average, according to a Poisson distribution. For question 3 & 4, assume there are 9 applicants arriving per 3 hours on average, accoring to a Poisson distribution. Answer the following questions: 1. If all applicants wait in a common line for the next available employee, how long would an applicant have to wait in line, on average, before he/she can be inter- viewed? 2. Suppose that each employee only conducts interviews for a specific department (i.e., receiving, shipping, production and HR), and each applicant applies for a job at a single one of these departments. Moreover, the number of applications is evenly divided over the departments. How long would an applicant have to wait in line, on average, before he/she can be interviewed? 3. During the winter times, less applications are received and the head of the HR de- partment has decided to use only three employees during this time. If all applicants wait again in a common line for the next available employee, how long would an applicant have to wait in line, on average, before he/she can be interviewed? 4. Again during winter, suppose that each employee only conducts interviews for a specific department, and each applicant applies for a job at a single one of these departments. The number of applications is, again, evenly divided over the depart- ments. However, since there are four departments hiring, and only three employees conduct interviews, the head of HR decides to let all applications for receiving and shipping be handled by a single employee. How long would an applicant for receiv- ing have to wait in line, on average? And a applicant for production floor? And applicants overall?