Question

at a single ticket booth, customers arrive randomly at a rate of x per hour.
the average line length is given by
F(x)= x^2/400-20x

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

Determine the range of rates at which customers can arrive before a second attendant is needed. Express your answer in interval form.

Answer 1

10 = (1/400) x^2 - 20 x ??? you did not use parenthesis so I assume this

4000 = x^2 - 8000 x

x^2 - 8000 x - 4000 = 0

x = [ 8000 +/- sqrt(64^10^6+16000) ]/2

x =

nah, impossible you must mean

f(x) = x^2 /(400 - 20 x)
10 = x^2 / (400 - 20 x)
4000 -200 x = x^2
x^2 + 200 x - 4000 = 0
x = [ -200 +/- sqrt(40000+16000) ]/2
= [ -200 +/- 236 ]/2
= 18, -218 ignore -218

0 </= x </= 18

Answer 2

thank you bottom is the correct way.