1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Need help to maxmize function

  1. Sep 1, 2010 #1
    1. The problem statement, all variables and given/known data

    I need help to maximize the below function:

    2. Relevant equations

    Maximize u(x, y) = x^α * y^β subject to Ax + By = m

    Any help is greatly appreciated!

    / Gekkoo
    Last edited: Sep 1, 2010
  2. jcsd
  3. Sep 1, 2010 #2


    User Avatar
    Homework Helper

  4. Sep 1, 2010 #3


    User Avatar
    Staff Emeritus
    Science Advisor

    I'm a big fan of "Lagrange Multipliers" but if you don't know that method, you could just write y= (m- Ax)/B so that [itex]x^\alpha*y^\beta= x^\alpha*(m-Ax)^\beta/B^\beta[/itex]. Now, do you know how to find maxima and minima for that?
  5. Sep 2, 2010 #4
    Thanks for your answers.

    1 Solve constraint for y:


    2 Plug into objective function:


    3 Diff w.r.t. x & equate to zero to get critical point:

    FOC: x^α*ln(x)*????=0

    4 Solve FOC for x:


    5 Plug that into constraint to get value for y:

    y = (m-A[????])/B

    6 Than I have a candidate solution & need to check SOC of objective function w.r.t x!

    But I fail to successfully derive FOC. Can anyone please help me out?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Need help to maxmize function