A new Broadway show is opening and people call in for tickets. There are 300 people waiting on hold on the phone when the operators start processing calls. The operators can handle 200 calls per hour at the beginning of the six-hour processing period, but steadily increase the number of calls per hour that they can handle as they become more adept at the ticketing process.
The graph of $P(t)$, as measured in calls per hour, shows the rate at which calls are processed. This is the dotted graph below. The graph of $C(t)$, as measured in calls per hour, shows the rate at which new calls are coming in. This is the solid graph below. $t$ is measured in hours from when the processing starts. Assume that no one hangs up when on hold.
Since the vertical axis is measured in calls per hour and the horizontal axis is measured in hours, the area of each individual rectangle on the grid created by the scales on the axes is equivalent to 100 calls per hour times 1 hour, or 100 calls.
At what time is the number of people on hold at its greatest number?
Which of the following choices describes how the total number of people on hold changes between times $t = 2$ hours and $t = 3$ hours?
How many calls still need to be processed after $t = 6$ hours?