Kuhn Tucker Conditions

[jsengabo]

Hello!
I was wondering if anyone could help me with this question?
I have struggled with it for days, but can not find a solution. The closest I got to was x=0 and y=1.
Another time i tried, and got Landa 1 = +-1 and Landa 2=0, but I could not find the solution for x or y.
Thanks in advance.

Best regards,
J

 

[Cubist]

I don't know about Kuhn Tucker Conditions.

But I was able to find a maximum value of f(x,y)=x/2-y at a point along the curve y=x+e^−x where x=log(2)/log(e).

I found this by cheating - I made a 3d plot of the area (using octave) and noticed that the maximum happened along the boundary y=x+e^−x. So I differentiated f(x, x+e^−x) with respect to x in order to find a stationary point.

This is probably not the method that you were taught, but hopefully it will give you a hint/ something to aim for. I'd be interested to see your working if you do this a different way.