At a Ticket Booth, Customers Arrive Randomly at a Rate $f ( x ) = \frac { x ^ { 2 } } { 400 - 20 x }$

Multiple Choice

At a ticket booth, customers arrive randomly at a rate of x per hour. The average line length is $f ( x ) = \frac { x ^ { 2 } } { 400 - 20 x }$ where $0 \leq x < 20$ To keep the time waiting in line reasonable, it is decided that the average line length should not exceed 6 customers. Solve the inequality $\frac { x ^ { 2 } } { 400 - 20 x } \leq 6$ to determine the rates x per hour at which customers can arrive before a second attendant is needed.

A) $0 \leq x \leq 17$
B) $0 \leq x \leq 18$
C) $0 \leq x \leq 16$
D) $0 \leq x \leq 19$