2
$\begingroup$

Okay, so we're given this equation $f(x,y)=x^2+y^2$ and the constraint is $x+2y-5=0$, and that $x>0$ and $y>0$,we have to find the minimum.

My answer is $(1,2)$, and my work is shown below.

Can anyone just check if I'm doing this correctly?

enter image description here

$\endgroup$
  • $\begingroup$ why dy/dx equals=-1/2,shouldn't it be dx/dy=1/2? also do you mean my final answer isn't correct? @ian $\endgroup$ – tehcoder Aug 14 at 11:26
  • 1
    $\begingroup$ It's easy to check the answer...writing $x=5-2y$ you can substitute for $x$ in $f(x,y)$ to get a function of one variable, which can then be minimized directly. $\endgroup$ – lulu Aug 14 at 11:27
  • $\begingroup$ My apologies, I misread your handwriting. I thought you wrote $\frac{\partial x}{\partial y}=\frac{\lambda}{2\lambda}$ but you wrote $\frac{2x}{2y}=\frac{\lambda}{2\lambda}$, which is correct. I've removed my other comments. (One of many reasons to learn to use MathJax!) $\endgroup$ – Ian Aug 14 at 11:36
  • $\begingroup$ Small editorial points : $\frac{\partial f}{\partial x}$ should be $\frac{\partial G}{\partial x}$. Same for the others derivatives. $\endgroup$ – Sesame Aug 14 at 11:56
  • $\begingroup$ @Ian its okay,but like my final answer is correct right? that the point would be (1,2) $\endgroup$ – tehcoder Aug 14 at 19:00

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.