Step 1:

The system of inequalities are and

Now graph the all of four constraints.

Draw the coordinate plane.

Now the inequality .

Graph the line .

 Since the inequality symbol is the boundary is included the solution set.

Graph the boundary of the inequality with solid line.

To determine which half plane to be shaded use a test point in either half- plane.

A simple choice is . Substitute in original inequality.

The statement is true.

Since the statement is true, shade the region contain point .

Now the inequality .

Graph the line .

Since the inequality symbol is the boundary is included the solution set.

Graph the boundary of the inequality with solid line.

To determine which half plane to be shaded use a test point in either half- plane.

A simple choice is . Substitute in original inequality.

The statement is true.

Since the statement is true, shade the region contain point .

Now the inequality .

Graph the line

Since the inequality symbol is the boundary is included the solution set.

Graph the boundary of the inequality with solid line.

To determine which half plane to be shaded use a test point in either half- plane.

A simple choice is . Substitute in original inequality.

The statement is false.

Since the statement is false, shade the region does not contain point .

Now the inequality .

Graph the line .

Since the inequality symbol is the boundary is included the solution set.

Graph the boundary of the inequality with solid line.

To determine which half plane to be shaded use a test point in either half- plane.

A simple choice is . Substitute in original inequality.

The statement is true.

Since the statement is true, shade the region contain point .

The feasible area looks like in the graph.

Observe the graph: The corner points are .