Charles runs an underground tutoring service, offering the writing of essay papers for students. He has hired 12 nerds to write papers for the clients he accumulates through word of mouth. Each nerd has the time to write 2 papers, including a bibliography for each, per week. The flow unit is the essay. The process consists of a client ordering, consulting with his or her assigned nerd for the writing of the essay, waiting for the paper, and then receiving the completed paper. On average, ordering a paper and receiving the paper is negligible. Consultation usually takes 45 minutes, and it takes a nerd 2 hours to write one paper. If a student wants his or her bibliography written, it takes a nerd an additional 25 minutes and has a contribution margin of $10. The average essay generates a contribution margin of $50 for Charles, and Charles hires a nerd for $8/hour.

1. If all clients want a paper including a bibliography, what is the capacity rate (paper per hour) of Underground Tutoring? Assume the due date for a paper is 1 week long.
2. At what rate ($/hour) is margin generated by Underground Tutoring if it is operating at capacity?
3. Assume that Charles establishes a subsidiary just for the bibliography work, supervised by his younger brother Ted and his team of "tutorers" from another school. Ted charges the same rate as Charles and has 16 employees working under him, who each have the time to write 2 bibliographies/week. Charles requests that all those that want bibliographies done, go immediately to Ted's Tutoring to pick up the finished papers. Assuming that all clients want both paper and bibliography, what is the capacity rate (papers/hour) of the total system (Charles and Ted)?
4. Following the assumptions given in c, at what rate ($/hour) is margin generated by the system if it is operating at capacity?