My linear programmer use the Simplex method.
$$\text {max}: c^T x\\ \text{s.t} \\ Ax \leq b \\ x \geq 0 $$
I have heard that it's possible to reforumlate the subject so it will solve for both uper bound limit and lower bound limit only for $Ax$. Can I write my subject too function as:
$$ \text {max}: c^T \begin{bmatrix} x_0\\ x_1 \end{bmatrix} \text{s.t} $$
$$ \begin{bmatrix} A &0 \\ 0 & A \end{bmatrix}\begin{bmatrix} x_0\\ x_1 \end{bmatrix} \leq \begin{bmatrix} b_u\\ -b_l \end{bmatrix} $$
But here is the hard part...this will not work. $$ \begin{bmatrix} x_0\\ x_1 \end{bmatrix} \geq 0 $$
Any suggestions? Or do you think I can run two simulations after each other? One with $b = b_u$ and one with $b_l$ ?
$b_l \leq Ax \leq b_u$ is $ \begin{bmatrix} A \\ -A \end{bmatrix}x \leq \begin{bmatrix} b_u\\ -b_l \end{bmatrix} $