Results 1 to 3 of 3

Math Help - Optimisation Problem

  1. #1
    Newbie
    Joined
    May 2013
    From
    Wollongong
    Posts
    3

    Optimisation Problem

    Hey guys, I having some problems with a math question for my uni homework and would greatly appreciate any assistance
    A company wishes to construct a pipeline connecting an oil refinery to an offshore drilling platform. The platform is situated 12km down the shore from the refinery and 11km out to sea. Constructing a pipeline in the ocean is more expensive than the one on land, so the company wants to run part of the pipeline along the shore and part of it through the ocean. The problem is to find the length of the pipeline along the shore which minimises the cost.
    1) Find expressions for the length of the pipeline along the shore and in the water in terms of the angle the pipeline makes with shore, theta
    2) What is the appropriate range of values that theta can have in this problem?
    3) It costs $60K per km to construct a pipeline on land and $120K per km to construct a pipeline in water. Write down an expression for the total cost (in thousands) to build the pipeline in terms of theta
    4) Find the value of theta that gives the minimum cost.
    5) Find the length of the land and water that minimise the cost and the cost itself.
    Cheers, any help would be greatly appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    4,163
    Thanks
    761

    Re: Optimisation Problem

    Hey rjd871.

    Hint: If the shore is approximately straight then you are going to have a right angle triangle with the right angle being the angle between the side of the "shore" portion of the piping and the side that connects the point of the drilling section to the nearest point on the shore.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jul 2012
    From
    INDIA
    Posts
    834
    Thanks
    209

    Re: Optimisation Problem

    Optimisation Problem-02-may-13.png
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Optimisation problem help
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 9th 2012, 08:45 AM
  2. Optimisation problem
    Posted in the Business Math Forum
    Replies: 0
    Last Post: February 24th 2011, 12:00 PM
  3. Optimisation problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 14th 2009, 01:23 AM
  4. optimisation problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 20th 2008, 08:10 PM
  5. Optimisation Problem?
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: July 31st 2008, 07:51 AM

Search Tags


/mathhelpforum @mathhelpforum