4. Consider the system of inequality constraints $Ax \ge b$ with
$$A = \begin{pmatrix} 9 & 4 & 1 & 9 & -7 \\ 6 & -7 & 8 & -4 & -6 \\ 1 & 6 & 3 & -7 & 6 \end{pmatrix}$$
and
$$b = \begin{pmatrix} -15 \\ -30 \\ -20 \end{pmatrix}$$
For
$$x = (7, -4, -3, -3, 3)^T$$
and
$$p = (3, 2, 0, 1, -2)^T$$
x and p, perform a ratio test to determine the maximum step length $\bar{a}$ such that $x + \bar{a}p$ remains feasible.