Simplex algorithm question with restraints

Question

How to perform simplex algorithm on the following: $$-x_1-2x_2 \rightarrow min \\ 4x_1+4x_2 \le 12 \\ x_1 \le 2 \ , x_2 \le 2 \\ x_1 \ge 0,x_2 \ge0$$ I would appreciate any hints how to solve this problem because i am a bit lost.

Answer 1

The minimum is reached at the vertices $(0, 0), (2, 0), (2, 1), (1, 2)$ or $(0, 2)$.

If $f(x_1, x_2)=−x_1−2x_2$ then

$f(0, 0)=0$

$f(2, 0)=-2$

$f(2, 1)=-4$

$f(1, 2)=-5$

$f(0, 2)=-4$

therefore the min this in $(1, 2)$.