Exercise A. Many people need to go to an office of the Department of Motor Vehicle...

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Exercise A. Many people need to go to an office of the Department of Motor Vehicle (DMV) to get new license plates or get their driver's licenses. Write an equation modeling the number of people P waiting in line. The assumptions are the following: a) Regardless of the length of the line, 10 people go to the DMV per hour. b) Some people want to minimize the time they will spend waiting in line. To do so, they check on the DMV website how long the line to a given office is and they choose to go to the office with the shorter wait time. Thus the inflow of these people is inversely proportional to the number of people already waiting in line. The proportionality constant is 0.5. c) The DMV employees tend to work slower when the line is short and faster when the line is long. The number of people exiting the DMV office is on average 0.25 the number of people who are waiting in line. Exercise A. Many people need to go to an office of the Department of Motor Vehicle (DMV) to get new license plates or get their driver's licenses. Write an equation modeling the number of people P waiting in line. The assumptions are the following: a) Regardless of the length of the line, 10 people go to the DMV per hour. b) Some people want to minimize the time they will spend waiting in line. To do so, they check on the DMV website how long the line to a given office is and they choose to go to the office with the shorter wait time. Thus the inflow of these people is inversely proportional to the number of people already waiting in line. The proportionality constant is 0.5. c) The DMV employees tend to work slower when the line is short and faster when the line is long. The number of people exiting the DMV office is on average 0.25 the number of people who are waiting in line.