Given the problem $$ \text{Minimize} \ \ \ \ c \cdot x \\ \text{subject to} \ \ \ \ Ax \leq b \\ x \geq 0, \ c \geq 0$$
show that an initial dual feasible solution is always present.
I know that the above minimum program can always be rewritten as the following dual program:
$$ \text{Maximize} \ \ \ \ b \cdot w \\ \text{subject to} \ \ \ \ A^Tw \leq c \\ w \ \ \text{unrestricted}$$
That's all I have at the moment. I don't see how this can tell me anything. Am I missing some important theorems?