1. Trucks arrive at a loading dock in a Poisson manner at the rate of 3.5 per day. The cost of waiting per truck per day is $168. A three-person crew that can load at a constant rate of four trucks per day costs $224 per day. Compute the total system cost for the operation.

2. Cars arrive at a toll plaza at the rate of 60 cars per hour. There are four booths, each capable of servicing 30 car per hour. Assume a Poisson distribution for arrivals and an exponential distribution for service time. If it costs $17.20 per hour to operate a toll booth and the waiting cost per car is $0.25 per minute spent at the plaza, how many booths should be operated to minimize total cost?

3. In a three-channel queuing system the arrival rate is 1 unit per time period and the service rate is 0.6 unit per time period. Determine the probability that an arriving unit does not have to wait.