Question

Find the feasible solution of the following inequations:

x - 2y ≤ 2, x + y ≥ 3, - 2x + y ≤ 4, x ≥ 0, y ≥ 0

Answer 1

First we draw the lines AB, CD and EF whose equations are x - 2y = 2, x + y = 3 and - 2x + y = 4 respectively.

Line	Equation	Points on the X-axis	Points on the Y-axis	Sign	Region
AB	x - 2y = 2	A(2, 0)	B(0,-1)	≤	origin side of line AB
CD	x + y = 3	C(3, 0)	D(0,3)	≥	non-origin side of line AB
EF	- 2x + y = 4	E(-2,0)	F(0,4)	≤	origin side of line EF

The feasible solution is shaded in the graph.