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

question 146

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) \(0 \leq x \leq 19\)

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