Results 1 to 2 of 2

Math Help - Calc Word Problem... Need Help!

  1. #1
    Member
    Joined
    Dec 2009
    Posts
    96

    Calc Word Problem... Need Help!

    I have been trying to figure out this problem. I have the answers in the back of the book and saw an attempt of it online, and still am not understanding what was done.

    The question says: Supertankers off-load oil at a docking facility 4 miles offshore. The nearest refinery is 9 miles east of the shore point nearest the docking facility. A pipeline must be constructed connecting the docking facility with the refinery. The pipeline costs 300,000 per mile if constructed underwater and 200,000 if over lands.

    a) Locate point B to minimize the cost of construction. (Point B forms a triangle with the docking station and point A)

    b) The cost of underwater construction is expected to increase whereas the cost of overland construction is expected to stay constant. At what cost does it become optimal to construct the pipeline directly to point A)

    If someone could help me with this problem that would be great. Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Apr 2010
    Posts
    8
    I can get you set up.

    The key is to let x be the distance from A to B. Then the rest of the shore distance is 9-x.

    The distance from B to the facility is the hypotenuse of the triangle.
    Use Phy. Th. to get the underwater distance given by sqrt(x^2+16). Thus the cost of underwater pipe is 300,000*(sqrt(x^2+16)). The shore pipe cost is then simply 200,000*(9-x)

    So total cost is: 300,000*(sqrt(x^2+16)) + 200,000(9-x) in dollars.

    You need to take the derivative and set equal to zero to find the optimum point x. This requires some algebra and squaring both sides. This is the answer to part a).

    The rest of the problem I leave to you.
    Last edited by palabine; April 12th 2010 at 08:55 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Pre-Calc Word Problem Help
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: February 12th 2011, 06:54 PM
  2. Calc word problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 19th 2009, 07:46 AM
  3. calc word problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: January 6th 2009, 04:11 PM
  4. Calc- Word Problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 31st 2008, 03:59 AM
  5. Calc Word Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 28th 2008, 03:02 PM

Search Tags


/mathhelpforum @mathhelpforum