1. Not finding help here? Sign up for a free 30min 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!

Multivariable Optimization Problem

  1. Feb 21, 2006 #1
    I need to "write the number 120 as a sum of three numbers so that the sum of the products taken two at a time is a maximum." I think this means that x+y+z=120 and xy+xz+yz=maximum. Can someone help me begin this problem?
     
  2. jcsd
  3. Feb 21, 2006 #2

    benorin

    User Avatar
    Homework Helper

    Would you be more confortable using the method of Lagrange Multipliers or using the substitution/partial derivatives=0 and the D=FxxFyy-Fxy^2 second derivative test thinggy?
     
  4. Feb 21, 2006 #3
    definitely using second derivative test thingy
     
  5. Feb 21, 2006 #4
    Got the idea. You set z=120-x-y and plug it into xy+xz+yz, which is then f(x,y). So you take the derivative of that, set the partials equal to 0, solve for x, solve for y, plug those back into z=120-x-y... and you get x, y and z equal 40.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?