91Ó°ÊÓ

First, we'll rewrite each inequality as an equation to graph them more easily: 1. \(x+y = 5\) 2. \(x = 10\) 3. \(y = 8\) 4. \(x = 0\) 5. \(y = 0\) To graph these inequalities, we can plot all points for which the inequalities are satisfied.

Next, we will shade the region that corresponds to the inequalities as follows: 1. \(x+y \geq 5\) - Shade the region above and including the line \(x+y = 5\) 2. \(x \leq 10\) - Shade the region to the left and including the line \(x = 10\) 3. \(y \leq 8\) - Shade the region below and including the line \(y = 8\) 4. \(x \geq 0\) - Shade the region to the right and including the line \(x = 0\) 5. \(y \geq 0\) - Shade the region above and including the line \(y = 0\) By shading these regions, we will find the region that fulfills all inequalities.

The region of interest is where all shading overlaps. We can see that this creates an enclosed polygon, so we can conclude that the region is bounded.

Now, we need to find the coordinates of the corner points where the lines intersect. We'll need to solve the system of equations for each intersection point. There are four possible corner points as follows: 1. Intersection of \(x+y = 5\), \(x = 0\), and \(y = 0\): Since this intersection doesn't exist, there's no corner point here. 2. Intersection of \(x+y = 5\) and \(x = 10\): \( \begin{aligned} x+y &= 5 \\\ x &= 10 \end{aligned} \) Solving this system of equations, we get \(x = 10\) and \(y = -5\). Since \(y \geq 0\), there is no corner point. 3. Intersection of \(x = 10\), \(y = 8\), and \(x+y = 5\): There is no intersection point for all three lines, so there is no corner point here. 4. Intersection of \(x = 10\), \(y = 8\), \(x = 0\), and \(y = 0\): Here, we only have intersections between \(x=10\) and \(y=8\), which is the point (10, 8). This is a corner point. Therefore, there is only one corner point which is (10, 8).