I have to solve the following task and I'm not sure if my thoughts are correct. It would be really great, if somebody could please help me:
Obtain the integral hull of $\lbrace z \in \mathbb{Z}: Bz \geq d_i \rbrace$ with $B=\begin{pmatrix} -1 \\ 1 \end{pmatrix}, d_1=\begin{pmatrix} -0.5 \\ 0.75 \end{pmatrix}$ and $d_2 = \begin{pmatrix} -1 \\ 0\end{pmatrix}$.
For $d_1$: The system $Bz \geq d$ is TDI, since there do always exist integer values for $y_1, y_2$ such that $y^TB=0$ and $y \geq 0$ (right?). Hence, I obtain Chvatal closure: $\begin{pmatrix} -1 \\ 1 \end{pmatrix}z \geq \begin{pmatrix} 0 \\1 \end{pmatrix}$. This polyhedron is empty and this won't change by applying Chvatal closure more often. Therefore, the integral hull is obtained.
For $d_2$: The system $Bz \geq d$ is TDI and the right hand side is integral, hence the integral hull is already given by $Bz \geq d$?