Step-by-Step Solution

1. Understanding the Constraints:<\/b> We are given the following constraints:
   • \(x \ge 0\)<\/li>
   • \(y \ge 0\)<\/li>
   • \(x + y \ge 4\)<\/li> <\/ul> <\/li>
   • Visualizing the Feasible Region:<\/b>
     • The inequalities \(x \ge 0\) and \(y \ge 0\) restrict the solution to the first quadrant.<\/li>
     • The inequality \(x + y \ge 4\) represents the region above the line \(x + y = 4\).<\/li> <\/ul> The line \(x + y = 4\) intersects the x-axis at (4, 0) and the y-axis at (0, 4). The region \(x + y \ge 4\) includes all points above this line in the first quadrant. <\/li>
     • Identifying Corner Points:<\/b> The feasible region is unbounded and extends infinitely in the first quadrant, above the line \(x + y = 4\). The corner points are the points where the boundary lines intersect. In this case, the boundary lines are \(x = 0\), \(y = 0\), and \(x + y = 4\).
       • Intersection of \(x = 0\) and \(x + y = 4\): Substituting \(x = 0\) into \(x + y = 4\) gives \(y = 4\). So, the point is (0, 4).<\/li>
       • Intersection of \(y = 0\) and \(x + y = 4\): Substituting \(y = 0\) into \(x + y = 4\) gives \(x = 4\). So, the point is (4, 0).<\/li> <\/ul> These are the only two corner points of the feasible region. <\/li>
       • Counting the Corner Points:<\/b> There are two corner points: (0, 4) and (4, 0). <\/li>