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Math Help - Max Min Calc Problem

  1. #1
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    Lightbulb Max Min Calc Problem

    Hey all,

    I am in a sticky situation at the moment involving a min/max calculus problem.
    the problem goes as follows.

    An offshore oil well must be connected by pipe to the refinery. The oil-well is 3 km off-shore. The refinery is on the coast, 6 km from the nearest point of land to the oil well. It costs $ S per kilometer to lay pipe along the shore, but U times as much per km to lay pipe underwater. The pipe may be laid either straight to the refinery or to an intermediate point on the coast then along the coast.

    Give the total cost as a function of the distance x between the point directly opposite the oil well and the place where the pipe comes ashore. This should be a formula involving x, S and U.


    Now I have considered a right angled triangle with U length on one side and S on the other and x being the hypotenuse. Now with that being the case, x^2 = u^2 + s^2 so x = sqrt(u^2 + s^2) with 0 < u < 3 and 0 < s < 6.

    However the question says cost as a function of the distance x between the point directly opposite the oil well and the place where the pipe comes ashore. This is the bit Iím struggling to comprehend. Any help would be greatly appreciated!
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  2. #2
    Grand Panjandrum
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    Re: Max Min Calc Problem

    Quote Originally Posted by jaykobhxc View Post
    Hey all,

    I am in a sticky situation at the moment involving a min/max calculus problem.
    the problem goes as follows.

    An offshore oil well must be connected by pipe to the refinery. The oil-well is 3 km off-shore. The refinery is on the coast, 6 km from the nearest point of land to the oil well. It costs $ S per kilometer to lay pipe along the shore, but U times as much per km to lay pipe underwater. The pipe may be laid either straight to the refinery or to an intermediate point on the coast then along the coast.

    Give the total cost as a function of the distance x between the point directly opposite the oil well and the place where the pipe comes ashore. This should be a formula involving x, S and U.


    Now I have considered a right angled triangle with U length on one side and S on the other and x being the hypotenuse. Now with that being the case, x^2 = u^2 + s^2 so x = sqrt(u^2 + s^2) with 0 < u < 3 and 0 < s < 6.

    However the question says cost as a function of the distance x between the point directly opposite the oil well and the place where the pipe comes ashore. This is the bit Iím struggling to comprehend. Any help would be greatly appreciated!
    Have you drawn a picture? U and S are costs per km of pipe how do you get to use them as lengths?

    The length of pipe under water is \sqrt{x^2+3^2} km then length of pipe on shore is (6-x) km.

    CB
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  3. #3
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    Re: Max Min Calc Problem

    Yes i have drawn a picture and just got totally bamboozalled!

    Give the total cost as a function of the distance x between the point directly opposite the oil well and the place where the pipe comes ashore. This should be a formula involving x, S and U. i'm still confussed on what to do there
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  4. #4
    Grand Panjandrum
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    Re: Max Min Calc Problem

    Quote Originally Posted by jaykobhxc View Post
    Yes i have drawn a picture and just got totally bamboozalled!

    Give the total cost as a function of the distance x between the point directly opposite the oil well and the place where the pipe comes ashore. This should be a formula involving x, S and U. i'm still confussed on what to do there
    How long is the pipe run under water?

    How long is the pipe run along the shore?

    How much do each of the runs cost?

    What is the total cost?

    CB
    Attached Thumbnails Attached Thumbnails Max Min Calc Problem-gash.jpg  
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  5. #5
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    Re: Max Min Calc Problem

    thanks for the picture

    so would the formula be u*sqrt(3^2 +x^2) + s*(x-6)?
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