Show that the solution set of the following system of linear inequalities is an unbounded region
Let us find the common region of all by plotting each inequality.
2x + y ≥ 8 …… (given)
Thus, for line,
2x + y = 8
x |
0 |
8 |
y |
4 |
0 |
Now, we know that (0,0) does not satisfy 2x + y ≥ 8
Thus, The region is away from the origin.
Now, x + 2y ≥ 10 …… (given)
Thus, for line,
x + 2y = 10
x |
0 |
8 |
y |
5 |
0 |
Now, we know that (0,0) does not satisfy x + 2y ≥ 10
Thus, The region is away from the origin.
Also, x ≥ 0 & y ≥ 0 implies that the region is in the first quadrant
Thus, the graph will be -
Hence, from the graph it is clear that the shaded region is unbounded.