MIN and MAX for funtions of two and three variables with constrainments

[jimbo71]

Homework Statement

see problem 4 and 5 attachment

Homework Equations

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!

 

[jimbo71]

i need help asap

 

[xaos]

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?