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OpenStudy (angelberina):
The speed of traffic through the Lincoln Tunnel depends on the density of the traffic. Let S be the speed in miles per hour and D be the density in vehicles per mile. The relationship between S and D is approximately S=42-(D/3) for D less than or equal to 100. Find the density that will maximize the hourly flow.
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OpenStudy (dumbcow):
hourly flow = speed*density \[F = D(42-\frac{D}{3}) = 42D - \frac{D^2}{3}\] maximize by setting derivative equal to 0 \[\frac{dF}{dD} = 42 - \frac{2D}{3} = 0\] \[D = 63\]
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