(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? I: (1) (ii) What is the average batch inventory? E (1 ) (iii) What is the average buffer inventory? E (1) (iv) What is the average time (in minutes) between a visitor arriving and being able to begin her tour? Em (v) What percentage of time is the elevator idle (i.e., not loading, traveling down, unloading, traveling up or being cleaned)? E (1 ) Question 2. (10 points) At one of the major National museums in Washington DC, 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 ground>bottom and 70 seconds to travel bottom> ground. * 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 ground>bottom; if the elevator needs to be full then loading starts 30x2 seconds = 60 seconds before the elevator starts to travel ground>bottom. Load > Ground>Bottom > Unload > Bottom>Ground > Cleaning > Idle > Load (a) What is the maximum rate (visitors per hour) at which the elevator can deliver visitors to the bottom? E (1) Visitors arrive at the Museum at a rate of one every 15 seconds, i.e., 240 per hour. Any visitor waiting to begin her tour, is at any point in time in exactly one of the following four categories: 1. inside the elevator traveling down; 2. inside the elevator waiting to exit the elevator after the elevator has reached bottom; 3. waiting to get into the elevator; 4. inside the elevator waiting for the elevator to travel down. Categories 1 and 2 constitute batch inventory. Categories 3 and 4 constitute buffer inventory. (b) Suppose that the Museum waits for the elevator to be full before running the elevator. You will want to draw an inventory (of visitors) buildup diagram to help with answering the questions that follow