Question

Find the feasible solution of the following inequation:

2x + 3y ≤ 6, x + y ≥ 2, x ≥ 0, y ≥ 0

Solve the following inequations graphically and write the corner points of the feasible region:

2x + 3y ≤ 6, x + y ≥ 2, x ≥ 0, y ≥ 0

Answer 1

First we draw the lines AB and CB whose equations are 2x + 3y = 6 and  x + y = 2 respectively.

Line	Equation	Points on the X-axis	Points on the Y-axis	Sign	Region
AB	2x + 3y = 6	A (3,0)	B (0,2)	≤	origin side of line AB
CB	x + y = 2	C (2,0)	B(0,2)	≥	non-origin side of line CB

The feasible solution is ΔABC which is shaded in the graph.