Results 1 to 2 of 2

Math Help - maximize minimum-> 2 functions, 2 variables

  1. #1
    chsn1982
    Guest

    maximize minimum-> 2 functions, 2 variables

    Hi,

    I have the following set of equations:

    C1 = X1*X2*log(a) + X1*(1-X2)*log(b) >= T
    C2 = X1*X2*log(c) + X2*(1-X1)*log(d) >= T

    a,b,c,d are known constants. Now I want:

    Max T over X1 and X2.

    any ideas???

    Thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Rebesques's Avatar
    Joined
    Jul 2005
    From
    At my house.
    Posts
    543
    Thanks
    12
    Let me see if I get this straight. You want to find maxT while C's are always greater than T?

    Then it must be maxT=min{C1,C2} for X1,X2. If your X's are defined throught the plane, just solve



    and compare the values to see which ones yield the minima. The min of these is maxT.

    If though your variables belong in some region, then use Lagrange coefficients.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: June 5th 2011, 04:57 PM
  2. maximize a sequence of functions
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 19th 2011, 07:07 AM
  3. Maximize the minimum value in a vector
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: August 5th 2010, 06:18 AM
  4. A unique minimum for a 2 variables function?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 13th 2009, 07:47 AM
  5. Replies: 2
    Last Post: June 4th 2009, 07:57 PM

/mathhelpforum @mathhelpforum