You need to graph the inequalities

x + y > 4

2x – 2y < 12 x - 4y > -16

For example, to graph the inequality

x+y>=4

replace it with the equation x+y=4. The latter defines a line. To draw this line you need two points the line is passing through. Set x = 0, then y = 4. Hence the first point is at (0,4). Similarly, the second point is at (4,0). Mark the points on the xy-plane and draw the line through them. The points whose coordinates satisfy the inequality x+y>=4 lie in a half-plane below or above that line. To determine the correct half-plane, substitute x=0, y=0 into the inequality. You will see that inequality fails. Therefore, the required half-plane doesn’t contain the origin, i.e. it is above the line.

Similarly, graph the half-planes corresponding to the other inequalities. They intersect in a convex polygon.

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