Quite a trivial question but it's bugged me. The problem I have to optimize is:
maximalise: $3x + 2y$
subject to:
$x + 3y \leq 17 $
$2x + y \leq 10 $
$x \leq 2$
$x, y > 0 $
I started to use the Lagrange multiplier with $λ_1$ and $λ_2$ for the first two constraints, but I realized that, as the $x$ and $y$ used are first order variables, the partial differentiation only gives me a system of two equations with $λ_1$ and $λ_2$, and no $x$ and $y$. That way, I can only find $λ_1$ and $λ_2$, but not $x$ and $y$.
So, could I use the Lagrange multiplier in some way so as to find the optimal solution? Or should it be done in another way?
Thanks for your time.