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Math Help - minimum cost

  1. #1
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    minimum cost

    an offshore oil well is 2 km off the coast. the refinery is 4km down the coast. laying pipe in the ocean is twice as expensive as on the land. what path should the pipe follow in order to minimize the cost? ok if the cost is based on distance times price, both are the same so it doesn't matter which they choose right? 4*P = 4p or 2*2p = 4p right?
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  2. #2
    Member
    Joined
    May 2008
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    It's helpful here to draw a right-angle triangle, ABD.
    A is the offshore well, D is the oil refinery.
    AB = 2 km
    BD = 4 km
    C is somewhere between B and D such that BC = x and CD = 4-x
    AC = path under the ocean = √(x+2)
    CD= path on land = 4-x
    Let y = cost per km on land

    Cost of AC = 2y*√(x+4)
    Cost of CD = y(4-x)
    Total Cost (C) = 2y√(x+4) + y(4-x)

    Hopefully you can take it from there.
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