f(x)= x^2/400-20x

Question

where 0<=x<20 to keep the wait in line reasonable, it is required that the average line should not exceed 10 customers.

 

determine the range of rates at which customers can arrive before a second attendant is needed 

Answer 1

This sounds like a queue theory predicate, but I can't make out the question.  There's a missing item explaining what f(x) is intended to describe. 

 

Range-wise, f(x) is basically a number that is -20 times x, offset by a smidge between 0 and 1.   

 

Doesn't sound like a reasonable number of tellers, or processing speed, or customer arrival speed...

 

If x is the number of tellers open, then perhaps f(x) is the resulting hourly burn-down on the queue? 

 

Assuming that guess is accurate, then the first teller (X=1) handles a little under 20 customers per hour. 

 

The question fragment "range of rates" doesn't make a whole lot of sense there, because it is rate differential over time that determines when the second one needs added.    30 clients per hour results in an overlong wait after one hour, for example.

 

Need a more specific problem to answer.