Determine lower and upper bound for decision variables in octagon analysis

[rajdeep87]

Consider the following trail where x,y,z are unsigned integers.
{x>=0, z<=5, x+y <= 10, y+z <=8}

How can we determine the lower bound and upper bound for x,y,z ?
x = [0,?], y=[?,?], z=[0,5];
Manually, this can be computed as x = [0,7], y=[0,3], z=[0,5];