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Math Help - (minimum/maximum problem) Minimum price for gasline

  1. #1
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    (minimum/maximum problem) Minimum price for gasline

    Hi all!

    I have the following math problem to be solved, and I really can't find it

    "A gasline has to be put from the coast to the city, begin and endpoint are determined. The costs along the coast are 750 dollar / kilometer, and through the city 1250 dollar / kilometer. Give the function to determine the minimum price - also give the minimum price."

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  2. #2
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    Re: (minimum/maximum problem) Minimum price for gasline

    Quote Originally Posted by zerox View Post
    Hi all!

    I have the following math problem to be solved, and I really can't find it

    "A gasline has to be put from the coast to the city, begin and endpoint are determined. The costs along the coast are 750 dollar / kilometer, and through the city 1250 dollar / kilometer. Give the function to determine the minimum price - also give the minimum price."
    I assume the distance "x" is along the coast.

    let C(x) be cost as a function of x

    C(x) = 750x + 1250\sqrt{120^2 + (160-x)^2}

    find C'(x) and minimize
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  3. #3
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    Re: (minimum/maximum problem) Minimum price for gasline

    Great, thank you!

    May I ask how you came to this solution? I have been staring at the picture for quite a while and failed to understand how to solve it.
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  4. #4
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    Re: (minimum/maximum problem) Minimum price for gasline

    Quote Originally Posted by zerox View Post
    Great, thank you!

    May I ask how you came to this solution? I have been staring at the picture for quite a while and failed to understand how to solve it.
    I didn't solve the problem ... just set it up.

    the expression for the length of the line through the city was determined using Pythagoras.
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