1) Vehicles on a highway arrive at a security checkpoint at a Poisson rate of 20 per hour. At the checkpoint, vehicles are inspected by a single security guard. The security guard can inspect vehicles at an exponential rate of 50 per hour. a. Find the probability that an incoming vehicle must wait in a security line. b. What is the average number of vehicles at the checkpoint? c. What is the average amount of time spent at the checkpoint? 2) There are plans to remodel the checkpoint from the previous problem so that more thorough checks can be performed. To accommodate the increased demands, the new checkpoint will allow for multiple guards. Because of the increased thoroughness of checks, it is expected that security guard inspections will now occur at a rate of 28 per hour. Additionally, traffic from a nearby checkpoint will be diverted to this new checkpoint, thereby raising the arrival rate to 55 vehicles per hour. We may still assume that that arrivals and service follow Poisson and exponential distributions, respectively. a. How many security guards must be used in this system so that the average time spent waiting in line at the checkpoint decreases from the system in problem 1? b. Find the total cost for the cases k=2, 3, and 4 security guards. Assume that security guards are paid $15/hour and that the cost of waiting is estimated to be $5/hour. Which option has the lowest cost? How does this compare to the total cost from problem 1