Show that the following system of linear inequalities has no solutin ` x+2y le 3, 3x +4y ge 12, x ge 0, y ge 1`.

Answer

N/a

Explanation

First inequation : ` x - 2y le 3`
Corresponding : `x - 2y = 3`
This line passes through the points A (3, 0) and `B (0, -(3)/(2))`. Join AB .
At point (0, 0), from the inequatioin, `0le3` (True )The solution of this inequation is that region of XY-plane dividing by line AB in which (0, 0) lies .
Second inequation : `3x+ 4y ge 12`
Corresponding equation : ` 3x + 4y = 12`
This lines passes through the points C(4, 0) and D (0, 3). Join CD.
At point (0, 0) , from the inequation, ` 0ge12` (False) The solution of this inequation is that region of XY-plane divided by line CD in which (0, 0) does not lie .
The solution of `x ge o is x = 0` and its right side.
The solution of `y ge 1 is y = 1 ` and its above.

`:.` The common solution of given inequation is shown by the shaded region.