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Homework Help: MIN and MAX for funtions of two and three variables with constrainments

  1. Mar 29, 2009 #1
    1. The problem statement, all variables and given/known data
    see problem 4 and 5 attachment

    2. Relevant equations

    3. The attempt at a solution
    see problem 4 attachement
    I found the gradient vectors of each and set fgrad=lamdbda*ggrad and used the constrainment equation to solve for all three variables. What is confusing me is I'm not sure what to do with the x,y,lambda values. How do they relate to the minimum and maximum values? I cannot attachemt my problem 5 attempt because it is too large of a file. but they are essential the same type of problem with different equations so if someone could please help me on number four i'll probably figure out number five. Also, can you check my that my algebra is correct in solving x,y,lambda for problem 4. Thank you!

    Attached Files:

  2. jcsd
  3. Mar 29, 2009 #2
    i need help asap
  4. Mar 29, 2009 #3
    first, if 2xy^4=L*2x then either case#1 x=0 or case#2 x does not =0. if not, then you can solve L=y^4.
    put this into the next equation to eliminate L. check both cases.

    second, if 4x^2y^3=L*4y then AGAIN, case#3 y=0 or case#4 y does not =0.

    eliminate L and put all these cases into the last equation which will probably give multiple solutions for each case. once you have a point x=? y=? put this into F(x,y)=? which one is smallest/largest?
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