Results 1 to 4 of 4

Math Help - Optimization help please?

  1. #1
    Member
    Joined
    Dec 2009
    Posts
    103

    Optimization help please?

    7. A model used for the yield Y of an agricultural crop as a function of the nitrogen level N in the soil(measured in appropriate units) is

    Y=\frac{kN}{1+N^2}

    where K is a positive constant. What nitrogen level gives the best yield?

    I thought all optimization problems follow a basic, constraint and then a formula form.
    I'm terrible at word problems, so I don't see where there is a constraint in this one?
    Please explain these problems to me. they drive me crazy.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by dorkymichelle View Post
    7. A model used for the yield Y of an agricultural crop as a function of the nitrogen level N in the soil(measured in appropriate units) is

    Y=\frac{kN}{1+N^2}

    where K is a positive constant. What nitrogen level gives the best yield?

    I thought all optimization problems follow a basic, constraint and then a formula form.
    I'm terrible at word problems, so I don't see where there is a constraint in this one?
    Please explain these problems to me. they drive me crazy.
    You're expected to realise that you start by solving dY/dN = 0.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,653
    Thanks
    1478
    Quote Originally Posted by dorkymichelle View Post
    7. A model used for the yield Y of an agricultural crop as a function of the nitrogen level N in the soil(measured in appropriate units) is

    Y=\frac{kN}{1+N^2}

    where K is a positive constant. What nitrogen level gives the best yield?

    I thought all optimization problems follow a basic, constraint and then a formula form.
    I'm terrible at word problems, so I don't see where there is a constraint in this one?
    Please explain these problems to me. they drive me crazy.
    Aren't you just looking for the maximum yield?

    If so...

    Y = \frac{kN}{1 + N^2}


    \frac{dY}{dN} = \frac{(1 + N^2)\frac{d}{dN}(kN) - kN\,\frac{d}{dN}(1 + N^2)}{(1 + N^2)^2}
    Last edited by mr fantastic; April 25th 2010 at 08:24 PM. Reason: Please leave something for the OP to do. If s/he needs more help, they can ask for it.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Dec 2009
    Posts
    103
    that's what I originally wanted to try... but I thought all optimization problems is supposed to have a constraint.
    And that seemed to be too easy. >_>
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. optimization help!
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 12th 2009, 12:54 AM
  2. Optimization
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 8th 2009, 02:09 PM
  3. Optimization
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 29th 2009, 10:56 AM
  4. optimization
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 12th 2008, 10:47 AM
  5. Optimization
    Posted in the Pre-Calculus Forum
    Replies: 0
    Last Post: October 13th 2008, 06:44 PM

Search Tags


/mathhelpforum @mathhelpforum