Multivariable Optimization Problem

  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. benorin

    benorin 1,026
    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. definitely using second derivative test thingy
  5. 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.
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