Difference constraints and constraint graphs Show the graph

Difference constraints and constraint graphs . Show the graph corresponding to the following system of inequalities -1 <= x - z <= 0, 0 <= y - z <= 1, -3 <= x - y <= -2. Is the system feasible? If

Solution

-1 <= x - z <= 0,

0 <= y - z <= 1,

-3 <= x - y <= -2.

Add all the three inequalities

-4 <= 2x-2z<=-1

i.e. -2<=x-z<=-0.5. This contradicts the first equation -1 <= x - z <= 0,

Hence system is not feasible.