Solve Problems 6 and 8. Please be sure to show ALL your work.
Problem 6
- Trucks are required to pass through a weighing station so that they can be checked for weight viola- tions. Trucks arrive at the station at the rate of 40 an hour between 7:00 p.m. and 9:00 p.m. Cur- rently two inspectors are on duty during those hours, each of whom can inspect 25 trucks an hour.
- How many trucks would you expect to see at the weighing station, including those being inspected?
- If a truck was just arriving at the station, about how many minutes could the driver expect to be at the station?
- What is the probability that both inspectors would be busy at the same time?
- How many minutes, on average, would a truck that is not immediately inspected have to wait?
- What condition would exist if there was only one inspector?
- What is the maximum line length for a probability of.
Problem 8
The parts department of a large automobile dealership has a counter used exclusively for mechan- ics’ requests for parts. The time between requests can be modeled by a negative exponential distri- bution that has a mean of five minutes. A clerk can handle requests at a rate of 15 per hour, and this can be modeled by a Poisson distribution that has a mean of 15. Suppose there are two clerks at the counter.
- On average, how many mechanics would be at the counter, including those being served?
- What is the probability that a mechanic would have to wait for service?
- If a mechanic has to wait, how long would the average wait be?
- What percentage of time are the clerks idle?
- If clerks represent a cost of $20 per hour and mechanics a cost of $30 per hour, what number of clerks would be optimal in terms of minimizing total co
