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Math Help - The cost per hour...

  1. #1
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    Question The cost per hour...

    The cost per hour for fuel to run a train is v^2/4 dollars,where v is the speed of train,in miles per hour.Other costs including labor are $300 per hour.How fast should the train travel on a 360 mile trip to minimise the total cost for the trip.
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    Quote Originally Posted by mathcalculushelp View Post
    The cost per hour for fuel to run a train is v^2/4 dollars,where v is the speed of train,in miles per hour.Other costs including labor are $300 per hour.How fast should the train travel on a 360 mile trip to minimise the total cost for the trip.
    The time taken for the trip is 360/v hours.

    Therefore C = \left( \frac{360}{v} \right) \cdot \left( \frac{v^2}{4} \right) + 300 \left( \frac{360}{v} \right).

    Minimise C.
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