Divvy is the dominant bicycle sharing company in Chicago. The company has a large number of stations scattered throughout the city. People can rent bikes from one station, ride them, and then return them to any station of their choosing (the destination station can be different from the origin station). Assume that each station has precisely 60 bicycle docks, but the number of bikes at the station varies throughout the day. The number of bikes at a station can never exceed the number of docks (because a dock is the only safe way to park a bike). If a person wanting to rent a bike comes to a station with no available bikes (i.e. a station with 60 empty docks), she leaves and tries to find some other method of transportation. Similarly, one cannot return a bike to a station where all docks are occupied (it must be taken to a different station). Let us zoom in on a single bike station in busy downtown Chicago that has 60 docks, from 6am-midnight, where the traffic patterns vary depending on the time of day. During the morning rush hour from 6am- 11am, people arrive at the station wanting to drop off a bike at a rate of 20 bikes/hour. From 11am- 4pm, this number drops to 15 bikes/hour, and from 4pm-midnight it drops further to 5 bikes/hour. The number of people wanting to rent a bike from the station from 6am-10am is 5 bikes/hour, from 10am-4pm its 10 bikes/hour, and from 4pm-midnight its 20 bikes/hour. For the following questions, assume that the station always starts with 30 bikes at 6am. You may assume rentals and returns occur uniformly throughout the hour. (a) Plot the inventory of bikes in the station from 6am-midnight. 100 90 80 70 60 50 40 30 20 10