A polyhedron in $mathbf{R}^2$

Consider the set in $mathbf{R}^2$ defined by a three affine inequalities:

$mathbf{P} = left{ x ~:~ 2x_1 + x_2 ge 3, ;; x_1 +2 x_2 ge 4 ;; 0 le x_1 le 5, ;; 0 le x_2 le 5right}.$

This set is a polyhedron, that is, a set of the form

with the component-wise inequality convention, and

The polyhedron mathbf{P} defined above. Each row of the matrix corresponds to a vector pointing outwards one of the facet of the polyhedron.