Problem $5$: For an escalator, there are $24$ rows with two steps in each row. The travel time for a step to go

from one end to the other is $30$ seconds.

a$)$ Suppose walking on the escalator is not allowed. What is the capacity of the escalator? $($in

customers$/$min$)$

b$)$ Suppose walking is allowed on the left side of the escalator. There must be at least one empty step

between two walking customers and the travel time of a customer to go through the escalator is $18$

seconds. What is the total capacity of the escalator? $($in customers$/$min$)$

c$)$ What if there are two empty steps between two walking customers? What is the new capacity?