During the Vancouver 2010 Olympics, in an effort to service the large inflow of tourists to the city, Translink set up a new route primarily for a fleet of Vancouver tour buses. The tours showcased popular Vancouver city highlights such as UBC, Stanley Park, Science World, and other popular attractions. You were hired as an expert for Translink to determine the number of buses that would be needed for this route. Before you began you needed to take into consideration several aspects of the process such as:

- A single tour bus takes exactly 2 hours to complete the tour.

- The tour starts and finishes at the UBC rose-garden pick-up point.

- Each tour bus has seating for 50 passengers, and room for another 30 passengers to stand. This route is busy much of the day, because tourists prefer to visit sites and attractions early in the day and attend Olympic events in the evening.

- Finally, Translink authorities want to show their Canadian hospitality and ensure they have enough capacity to handle peak customer loads so that no demand is unmet.

a. Assuming there are only 2 buses servicing this new route, what is the cycle time between each completed tour?

b. Translink does not want anybody to wait any longer than 6 minutes to catch a tour-bus. How many buses will be required to service this route to meet this requirement?

c. Now assuming Translink wants to service the route with the number of buses that you have calculated in number 2. What is the maximum amount of passengers that can be accommodated at a single point in time on the tour route?

d. The buses operate from 8am to 8pm. The pick-up point for the tour is at UBC rose-garden, where the tour begins and ends. From 8am until noon, tourists arrive at a rate of 450 passengers per hour. From noon to 2pm tourists arrive at the rate of 1000 passengers per hour. From 2pm until 8pm, passengers arrive at a rate of 700 each hour. The tour-bus system can pick up tourists at a rate of 800 passengers per hour. How many tourists do you expect to see waiting to get on a tour-bus at the rose-garden at 10am? At 1:30pm? At 5:45pm? Hint: Create a plot/graph/diagram of the number of tourists waiting as a function of time.