A shop is open 9 AM - 7 PM. The function r(t), graphed above, gives the rate at which customers arrive (in people/hour) at time t, where t measures time in hours since 9 AM. Suppose that the salespeople can serve customers at a rate of 85 people per hour. Answer the following questions:

Graph starts at (0,0). Reach Maximum at (6,110) and ends at (11,0)
A. At what time will people begin having to wait in line before getting served (because the volume of people arriving has become too great)?
equation editorEquation Editor hours after opening.

B. When is the line longest? Answer:
equation editorEquation Editor hours after opening.
C. How many people are in the line at the time when it's the longest?
Answer:

D. When does the line vanish?
Answer: hours after opening.

1 answer

A. looks like you need to find where r(t) > 85
B. probably where r(t) is a max
C. the area under the curve from A to t : r(t)-85t
they are backing up during this interval.
D. See C, where the area under r(t)-85t = 0

Actually, line length is hard to say. Just because they can serve 85 per hour does not mean that they can serve them all at once, right? I suspect there is a bit more to this than a simple graph can capture.
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