Show that the solution set of the following system of linear inequalities is an unbounded region ` 2x+y ge 8, x+2y ge 10, x ge 0, y ge 0`.

Explanation

First we draw the graph of `2x+y ge 8`
Consider the line graph of ` 2x + y ge 8`
Now , `2x+y = 8 rArr x/4+y/8 = 1`
This line meets the axes at A(4, 0) and B(0, 8).
Clearly, the line AB represents 2x + y = 8.
It is also clear that (0, 0) does not satisfy `2x + y le 8`
Thus, the line AB and the part of the plane not containing 0(0, 0) represent the solution of the inequation `2x + y ge 8`
(ii) Next, we draw the graph of `x + 2y ge 10`
Consdider , the line x+2y = 10
Clearly, the points C(O, 5) and D(2, 4) lie on this line.
Also ,(0,0) does not satisfy of `x+ 2y ge 10 `
So, the line CD and the part of the plane not containig O (0,0) represent the solution set of `x+ 2y ge 0`
(iii) `x ge 0` is repesented by the x-axis and the plane above the x-axis .
It is clear form the above graph that the solution set of the given indequations is an unbounded region , shown by the shaded region .