How to solve a Robust Linear Program problem?

Question

How to solve a Robust problem? For example if I have the following Robust LP.

minimize $\beta$

subject to

$3x_1+4x_2 \leq7$

$3x_1 \leq7$

$x_1 \geq 0$

$x_2 \geq 0$

$-x_1+4x_2\leq\beta$

$x_1+4x_2\leq\beta$

How should I tackle this problem?

Answer 1

You have two upper bounds for $\beta$, but no lower bound. I think the minimum is $\beta = -\infty $