Q.Find the feasible solution of the following inequations graphically : $x - 2y \le 2,\ x + y \ge 3,\ -2x + y \le 4,\ x \ge 0,\ y \ge 0$

Draw the boundary line of each constraint ($x-2y\le2,\ x+y\ge3,\ -2x+y\le4,\ x\ge0,\ y\ge0$) using its intercepts, shade the half-plane each inequation demands (test the origin, or another convenient point, in each), and darken the region common to all of them. The corner points of this common region are found by solving each pair of adjacent boundary lines simultaneously and keeping only the intersections that also satisfy every other constraint. Doing this here gives the vertices (0, 3), (0, 4), (\tfrac83, \tfrac13), forming a triangular corner of an UNBOUNDED region. Unlike I1–I5, this region is genuinely unbounded: beyond the vertex $(0,4)$ the boundary $-2x+y=4$ and beyond the vertex $\left(\tfrac83,\tfrac13\right)$ the boundary $x-2y=2$ both extend indefinitely to …

Draw all boundary lines, shade each half-plane by the test-point method, take the common overlap, then find its corner points by solving the boundary equations pairw …

Including a line-intersection point that fails one of the OTHER constraints as a 'vertex' is the most common error — every candidate corner point must be checked aga …