Can the optimal value of the primal problem of a linear program ever be less then zero?
An example is: minimize $C=2x_1 +3x_2$ Subject to: $3x_1+4x_2 \leq 5$. Obviously, $x_1$ and $x_2$ are free variables so the optimal solution is either 0 or $-\infty$.
Just wondering which it would be and why it could or couldn't be negative infinity.
