I have the following problem:
You have max(x2+y2) which his restrained on the set x2+y2=1
1) Prove that this problem has solution.
2) Solve the Lagrange problem
3) Find the optimal value of the objective function
Here my answers:
1) It has a solution because the function is continous and it's restraint is a closed and bounded set. Therefore the extrem value theorem tells us that it attains a minimum and a maximum value at least once.
Now I take the three derivatives, set them zero and solve the system of equations, so I get the points:
(-+1,0) and (0,+-1) and (+-21/2/2,+-21/2/2)
So the first two points are the maximum while the third point is the minimum value.
3) I don't really understand the question here. What could be meant by optimal value?
I can see that the value of the function is 1 at its maximum and 1/2 at its minimum. - Could that be the answer?
Thank you for your help!