1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook