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    jessica334's Avatar
    jessica334 Posts: 3, Reputation: 1
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    #1

    Oct 11, 2009, 06:25 AM
    Minmize and max
    The cost of fuel to run a locomotive is propotional to the 3/2 power of the speed.At a speed of 23 miles per hour, the cost of fuel is $50 per hour. Other costs amount to $100 per hour.
    a) find the speed that will minimize the cost per mile.
    b) what is the cost of a 300-mile trip at the optimal speed?
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #2

    Oct 11, 2009, 01:01 PM
    Use the given info to find k in

    Where C=cost and s=speed.







    To find the cost per mile, divide by s. Don't forget the $100 additional cost.





    Differentiate:



    Set to 0 and solve for s and we get:



    That is the optimal speed.

    Now, can you finish the second part?

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