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Math Help - Optimization Problem

  1. #1
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    Optimization Problem

    I'm really confused on this problem[GVIDEO][/GVIDEO]

    A company wishes to run a utility cable from point A on the shore to an installation at point B on the island. The island is 6 miles from the shore (point O) It costs $3000 per mile to run the cable on land and $5000 per mile underwater. Assume that the cable starts at A and runs along the shoreline, then angles and runs underwater to the island. Let x represent the distance from O at which the underwater portion of the cable begins, and the distance between A and O be 9 miles.

    1. Write the total cost C as a function of x.
    2.Find the point at which the line should begin to angle in order to minimize the total cost.
    3. what is the minimum cost?
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  2. #2
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    You want to find where to put point P so that
    $3000 * length of AP + $5000 * length of PB is a minimum.
    Attached Thumbnails Attached Thumbnails Optimization Problem-shore-problem.bmp  
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