Jake is running a new ski lift at your mountain. Today is Jake's first day on the job. Skiers are expected to arrive at the loadign station fo Jake's lift at the rate of 20 every minute in a Poisson arrival pattern, and are served first-come, first-serve manner. Jake can dial up de speed on the lift at the start of each day, but once he sets this rate at the start of the day, he cannot change it any more during the day.

Part 1: On his first day, Jake decides to put the lift at its maximum setting of 4000 skiers lifted per hour, to see what the machine can do. What is the average utilization og the lift that day, the average number of skiers waiting in line, and the average time spent waiting in line at Jake's lift?

Part 2: At the end of his first day, Jake is reprimanded by his boss, because to many skiers got hurt riding on his lift because of the speed. On his second day, Jake decides to decrease the speed. He decided that since skiers arrive at the rate of 20 every minute, that he will run the lift speed just higher thatn the skier arrival rate, and run the lift at 21 skiers lifted every minute. What is the average utilization of the lift, the average number of skiers waiting in line, and the average time waiting in line at Jake's lift?

Part 3: What happens if Jake decides on his third day to run the lift at the rate of 20 skiers lifted every minute?