Results 1 to 5 of 5

Math Help - Mathematical Model

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    7

    Mathematical Model

    With 1000ft of fencing, a person wishes to fence a field into three parts as shown in the diagram. (The diagram is just a rectangle with it sectioned into three portions, y being height, x width)

    How would you determine the values of x and y that give the maximum area?

    ** I tried to write down y in terms of x for a previous question, and I got a(x)=-x^2+500 but I really don't know if I even did that correctly.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Nov 2008
    Posts
    61
    I'm going to assume that it's split into three along its height, if it's not then just switch x and y in my explanation.

    We know then that the total perimeter is 4x+2y=1000 or y=500-2x. The area is A=xy=x(500-2x)=500x-2x^2.

    Differentiate that and you'll find your answer.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2009
    Posts
    7
    Thanks. Yes, its split along its height (the lines are vertical). For the perimeter I got 2y+2x=1000, though. Does it become four because of the split sections? I wasn't sure what to do with that.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Nov 2008
    Posts
    61
    Is it like my sketch below? If so then you have to switch x and y in my previous post. The total perimeter is 2x+4y=1000 (there's 2 horizontal lines and 4 vertical lines) and then A=500y-2y^2.
    Attached Thumbnails Attached Thumbnails Mathematical Model-sketch.bmp  
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Feb 2009
    Posts
    7
    Yes, it's like your sketch, thanks!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. mathematical model
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: July 2nd 2010, 01:11 PM
  2. mathematical model
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: February 23rd 2009, 07:57 PM
  3. mathematical model
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: November 12th 2007, 10:57 PM
  4. Challenging Mathematical Model
    Posted in the Advanced Applied Math Forum
    Replies: 3
    Last Post: November 7th 2007, 09:02 PM
  5. Mathematical Model of a Catenary
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: August 19th 2007, 08:42 AM

Search Tags


/mathhelpforum @mathhelpforum