I just started learning LP and I saw this Q in my textbook:
$$ min : -x -y \\ S.T. : x + 2y \le 3, 2x +y \le 3, x \ge 0, y \ge 0 $$
It is easy to see that the polygon created from these constraints can't have a negative coordinate. In my textbook it says the answer is $(0,0)$ since $-0 -0 = 0$ and this is the minimum value of the target function (i.e. $f(x,y) = -x -y$).
Why is that the minimum? If I choose any other values (S.T. the constraints are satisfied) I can get, for example, $(1,1)$ which will result in $-1 -1 = -2 < 0$!
Another thing that I don't understand - would there be a difference if my function was different? If the min is $(0,0)$ - wouldn't it be the case for any other $f(x,y) = a*x + b*y$ for any other $a,b$?