a) In a COVID vaccination center, the process is split up in several stages. The first stage is to register your information and receive explanations. This is done by clerks and takes 6 minutes per person. The second stage is the administer the vaccine. This is done by nurses and takes 3 minutes per person. Finally, each person has to wait for 15 minutes before leaving, to make sure there are no immediate side effects. This must be done in a specially designed waiting room, monitored by a guard. There are 12 chairs in this waiting room. Furthermore, there are 6 clerks and 5 nurses. Vaccination is done by appointment for specific slots. Given the current setup of the process and assuming no uncertainty and that everyone shows up, how many people should be invited per hour, given that the aim is to maximize the number of people that get vaccinated. Clearly support your answer and show the calculations