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Oil Refinery: Optimization Problem

  1. Sep 27, 2009 #1
    1. The problem statement, all variables and given/known data

    A drilling rig 12 miles off shore is to be connected by a pipe to a refinery onshore, 20 miles down the coast from the rig. If underwater pipe costs $40,000 per mile and land based pipe costs $30,000 per mile what value of x and y would give the least expensive connection?




    3. The attempt at a solution

    I have no idea on where to start. I know I need to find a relevant equation, differentiate it, then set it to 0, and finally show that it is a relative minimum, but I'm having trouble finding the relevant equation. I recreated the image that was in my textbook, and attached it to this post.
    Thanks for your time.
     

    Attached Files:

  2. jcsd
  3. Sep 27, 2009 #2
    First replace x with an expression that has y, using the Pythagorean theorem, so you have to work with just one variable.

    The land distance will be 20-y miles and the land pipe costs $30,000 per mile, so the cost for land pipe will be $30,000(20-y). Find another expression like that for the underwater pipe cost, then add the two to get a function of y for the cost.
     
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