Results 1 to 3 of 3

Math Help - optimization w/ implicit differentiation

  1. #1
    Newbie
    Joined
    Aug 2009
    Posts
    19

    optimization w/ implicit differentiation

    I need help in the setup of this word problem: Find two positive integers whose sum is 50 and whose product is as large as possible.
    I set it up as x+y=50 and xy=as large as possible.
    I know that these are usually done by solving for one of the variables, substituting it into the other problem, taking the derivative, finding the absolute max, blah blah, but I'm confused because the second equation has an indeterminate answer. Any help on how to set this up would be awesome!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Sep 2010
    Posts
    86
    To wrap this up: You maximize xy s.t. x+y = 50.

    Thus x = 50 - y and you can maximize y(50-y) = 50y - y^2 and the solution to this is determinate since it is implicitly constrained by your first equation.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2009
    Posts
    19
    Ah, so i get 50x-x^2 f'(x)=50-2x x=25 which makes y=25 as well which is correct! Thanks a ton!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Implicit Differentiation
    Posted in the Calculus Forum
    Replies: 10
    Last Post: January 19th 2011, 11:59 AM
  2. Replies: 2
    Last Post: July 26th 2010, 05:24 PM
  3. Implicit differentiation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 6th 2010, 02:33 AM
  4. Implicit differentiation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: July 20th 2007, 12:46 PM
  5. Help w/ implicit differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 20th 2007, 07:29 AM

Search Tags


/mathhelpforum @mathhelpforum