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!

Lagrange with Two Constraints

  1. Feb 26, 2017 #1
    1. The problem statement, all variables and given/known data

    kuGWwwg.jpg

    2. Relevant equations

    Partials for main equation equal the respective partials of the constraints with their multipliers

    3. The attempt at a solution

    UmkCpuX.jpg

    Basically I am checking to see if this is correct
    I am pretty sure that 25/3 is the minimum but I am not sure how to find the maximum
    The max an min at the bottom can be ignored or replaced with minimum
    I have a lot to do today to prepare for midterms so any help would be much appreciated
     
  2. jcsd
  3. Feb 26, 2017 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Your final solution looks OK, but I did not check the rest because I generally do not look at solutions given as posted images.

    You should think about why your solution method does not give you a maximum.
     
    Last edited: Feb 26, 2017
  4. Feb 26, 2017 #3
    So is 25/3 the only extrema and a minimum?
     
  5. Feb 26, 2017 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You tell me. But more importantly, what is the reason?
     
  6. Feb 26, 2017 #5
    Yes? because the function is not bound and is continuous?
     
    Last edited: Feb 26, 2017
  7. Feb 26, 2017 #6

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Right, and because the feasible region (the set of allowed ##(x,y,z)## values) is unbounded. We can find feasible points ##(x,y,z)## with ##x,z \to -\infty,\: y \to +\infty## (and opposite); and of course, ##f \to +\infty## for such points.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted