a. Problem 2: My recent trip to Washington DC. reminded me of how good we have it here in Dalton, GA. The traffic was horrible! Waiting in traffic provided me with ample time to contemplate how queuing theory could be used to evaluate a toll booth operation. During rush hour I estimate that cars arrive at 1400/hr. and there are 7 toll booths that each can process 250 cars/hr. What is the average number of cars in line waiting for a chance to pay their toll? b. What would be the average time that a vehicle must wait to get through the system? How many operators would be necessary if 30 seconds is more than enough time to expect to wait in line and pay a toll? d. If the cost of employing each toll operator is $20/hr and a commuter's time is valued at $5/hr, what case can you make for employing more operators? Assume this situation exists 8 hours a day 5 days a week with a 50 week work year. (I would express this as a ratio of the cost to commuters versus the cost of the additional operator(s).) c. Problem 3: Suppose the toll stations described in the prior question were replaced with a single lane that used an electronic debit card. Cars are estimated to arrive according to a Poisson distribution with a mean rate of 1,400 vehicles per hour. It will take exactly 2.25 seconds to verify the debit card How much time would you expect the traveler to wait in line, pay with the debit card, and leave? b. How many cars would you expect to see in the system? How much money could the city afford to spend on the station each year? (Assuming it replaces the existing number of stations described the prior question.) a