At one of the major National museums in Washington D.C., all visitors begin their tour by riding a VERY large elevator down to the lowest level. This allows them to view the exhibits in sequence as they walk from the lowest level basement to the ground floor. And is part of the experience. The elevator can hold up to 30 visitors. Loading the elevator takes 2 seconds per person; unloading the elevator takes 2 seconds per person. It takes the elevator 50 seconds to travel groundbottom and 70 seconds to travel bottomground. After the elevator reaches ground, it needs 60 seconds of cleaning time. The elevator then stays idle till it is time to start loading. Loading starts just in time. For example, if the elevator is to wait for 20 visitors then loading starts 20x2 seconds = 40 seconds before the elevator starts to travel groundbottom; if the elevator needs to be full then loading starts 30x2 seconds = 60 seconds before the elevator starts to travel groundbottom.

(a) What is the maximum rate (visitors per hour) at which the elevator can deliver visitors to the bottom? 

(i) What will be the time (in seconds) between when the elevator starts to travel down and when it

starts to travel down the next time? In other words, how often does the process repeat itself?

(ii) What is the average batch inventory?

(iii) What is the avereage buffer inventory?

(iv)What is the average time (in minutes) between a visitor arriving and being able to begin her tour?

What percentage of time is the elevator idle (i.e., not loading, traveling down, unloading,