The teacher gave us some problems on the board for us to jot down. He said it would prepare us with the final.

Problem:

Optimize the function subject to the constraint

I am not 100% sure what optimize means and if Lagrange multiplier applies but this is what i have so far.

Combining we have:

(1)

(2)

(3)

Solving (1) for x:

(4)

(5)

(6)

Now, add in (4),(5), and (6) for the constraint

then

So, at this point i am stuck. I don't know how to finish.

I don't even know if i was suppose to use Lagrange multiplier or if its correct up to that point?

If someone could let me know if i did the problem correctly and help me finish?

Thank you so much.