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Math Help - Optimization Problem

  1. #1
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    Optimization Problem

    The problem is to figure out what speed a truck driver should travel in order to minimize cost on a 1600 mile round trip.
    Given Costs:
    $22.50/hour for driver
    $0.27 for wear on the truck
    $v/140 for fuel where v=speed in miles per hour

    What speed between 45-60mph should the driver travel to minimize cost.

    I thought this would be easy, but I can't seem to get the right answer.

    My first thought was to determine the cost of the driver in terms of speed (v) by dividing the number of miles (1600) by speed (v). Giving me of course 1600v. Then I would add it to the cost of the fuel and wear (which is a fixed cost anyway and shouldn't really be considered), then take the derivative, equate it to zero, find the min/max.

    But the number I am coming up with is incorrect. Can anyone tell me where I am going wrong?

    Many thanks in advance!
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  2. #2
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    Re: Optimization Problem

    Quote Originally Posted by ScreamingEmu View Post
    The problem is to figure out what speed a truck driver should travel in order to minimize cost on a 1600 mile round trip.
    Given Costs:
    $22.50/hour for driver
    $0.27 for wear on the truck
    $v/140 for fuel where v=speed in miles per hour

    What speed between 45-60mph should the driver travel to minimize cost.

    I thought this would be easy, but I can't seem to get the right answer.

    My first thought was to determine the cost of the driver in terms of speed (v) by dividing the number of miles (1600) by speed (v).
    Giving me of course 1600 / v. <--- typo
    Then I would add it to the cost of the fuel and wear (which is a fixed cost anyway and shouldn't really be considered), then take the derivative, equate it to zero, find the min/max.

    But the number I am coming up with is incorrect. Can anyone tell me where I am going wrong?

    Many thanks in advance!
    Your considerations are OK.

    But since v \in [45,60] you have to take into account that the extreme values could be found at the borders of the domain.

    BTW: Which value did you find for v?
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