I have the following problem: $ max_{x,y} \ x + y $
subject to
$ 2x + y \leq 1 $
$ x + 3y \leq 3 $
$ x,y \geq 0 $
How to find the dual of this problem using the Lagrangian?
I have done the following steps:
Step 1: Rewriting the problem as a minimization
$ - \ min_{x,y} \ -x - y $
subject to
$ 2x + y \leq 1 $
$ x + 3y \leq 3 $
$ x,y \geq 0 $
Step 2: Formulating the Lagrangian
$ L(x,\lambda) = -x - y + \lambda_1(2x+y-2) + \lambda_2(x + 3y -3) - \lambda_3 x - \lambda_4 y \ \ \ \ \ \ \ \ \ \lambda_i \geq 0 $
Step 3: In order to find the dual I have to minimize the lagrangian
I am stuck in this step. How do I proceed?