### Graphing the Feasible Region for a System of InequalitiesTo graph the feasible region for the following system of inequalities, we will draw a polygon around the feasible region by following these steps:\[\begin{cases}x + y \leq 11 \\-x + y \leq 2 \\y \geq 4 \end{cases}\]Instructions:1. Plot the lines corresponding to each inequality on the graph.2. Identify the region satisfying all inequalities.3. Shade or mark the feasible region.#### Step-by-Step Solution1. **Graph the Line \(x + y \leq 11\)**: - The line \(x + y = 11\) can be plotted by finding the intercepts. - x-intercept: \((11, 0)\) - y-intercept: \((0, 11)\) - Draw the line through these intercept points.2. **Graph the Line \(-x + y \leq 2\)**: - The line \(-x + y = 2\) can also be plotted by finding the intercepts. - x-intercept: \((-2, 0)\) - y-intercept: \((0, 2)\) - Draw the line through these intercept points.3. **Graph the Line \(y \geq 4\)**: - The line \(y = 4\) is a horizontal line through \(y = 4\). - Shade the region above this line (where \(y \geq 4\)).After graphing, the feasible region will be the overlapping region that satisfies all three inequalities. This region can then be highlighted by drawing a polygon around it, using points of intersection as vertices.#### Diagram ExplanationThe graph consists of a standard Cartesian coordinate plane with axes ranging from -1 to 11 on both the x and y axes. - The x-axis represents the possible values of \(x\) from -1 to 11.- The y-axis represents the possible values of \(y\) from -1 to 11.By following the above steps, identify the overlapping region to find the feasible region and highlight it.Take some time to graph these inequalities on your graph paper and shade the feasible region to visualize the solution properly.This explanation will help in ensuring that the concept of graphing

Answered: Image /qna-images/answer/694543dd-a857-4e06-9852-b0ab11ca2c8e.jpg

Graph the feasible region for the follow system of inequalities by drawing a polygon around the feasible < 11 x + y -x+y region. Click to set the corner points. Y H 10 9 % 6 8 7 6 5 4 3 2 1 -1 f-1 1 2 3 4 5 6 7 8 9 10 11 2 > 4

Graph the feasible region for the follow system of inequalities by drawing a polygon around the feasible < 11 x + y -x+y region. Click to set the corner points. Y H 10 9 % 6 8 7 6 5 4 3 2 1 -1 f-1 1 2 3 4 5 6 7 8 9 10 11 2 > 4

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

### Graphing the Feasible Region for a System of Inequalities

To graph the feasible region for the following system of inequalities, we will draw a polygon around the feasible region by following these steps:

\[
\begin{cases}
x + y \leq 11 \\
-x + y \leq 2 \\
y \geq 4
\end{cases}
\]

Instructions:
1. Plot the lines corresponding to each inequality on the graph.
2. Identify the region satisfying all inequalities.
3. Shade or mark the feasible region.

#### Step-by-Step Solution

1. **Graph the Line \(x + y \leq 11\)**:
- The line \(x + y = 11\) can be plotted by finding the intercepts.
- x-intercept: \((11, 0)\)
- y-intercept: \((0, 11)\)
- Draw the line through these intercept points.

2. **Graph the Line \(-x + y \leq 2\)**:
- The line \(-x + y = 2\) can also be plotted by finding the intercepts.
- x-intercept: \((-2, 0)\)
- y-intercept: \((0, 2)\)
- Draw the line through these intercept points.

3. **Graph the Line \(y \geq 4\)**:
- The line \(y = 4\) is a horizontal line through \(y = 4\).
- Shade the region above this line (where \(y \geq 4\)).

After graphing, the feasible region will be the overlapping region that satisfies all three inequalities. This region can then be highlighted by drawing a polygon around it, using points of intersection as vertices.

#### Diagram Explanation
The graph consists of a standard Cartesian coordinate plane with axes ranging from -1 to 11 on both the x and y axes.

- The x-axis represents the possible values of \(x\) from -1 to 11.
- The y-axis represents the possible values of \(y\) from -1 to 11.

By following the above steps, identify the overlapping region to find the feasible region and highlight it.

Take some time to graph these inequalities on your graph paper and shade the feasible region to visualize the solution properly.

This explanation will help in ensuring that the concept of graphing

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