### Graphing the Feasible Region for the System of Inequalities To graph the feasible region for the following system of inequalities, draw a polygon around the feasible region based on the corner points identified on the graph. **System of Inequalities:** 1. \(2x + 5y \leq 30\) 2. \(4x + 5y \leq 40\) 3. \(x \geq 0\) 4. \(y \geq 0\) **Graph Details:** - The graph is a coordinate plane with \(x\) and \(y\) axes, extending from -2 to 10 on the x-axis and from 0 to 10 on the y-axis. - The inequalities will form boundary lines on the graph, and the area where all inequalities overlap will be shaded to show the feasible region. - The feasible region is the set of all points \((x, y)\) that satisfy all the given inequalities simultaneously. - Use the interactive graph tool to draw and adjust the polygon by selecting the corner points of the feasible region. **Instructions:** 1. Identify the critical points of intersection between the boundary lines. 2. Click on these points within the graph area to form a closed shape that represents the feasible region. 3. Once the polygon encloses the feasible region, click "Submit Question" to confirm your graph. This exercise demonstrates graphing systems of linear inequalities and visualizing solutions on a coordinate plane.
### Graphing the Feasible Region for the System of Inequalities To graph the feasible region for the following system of inequalities, draw a polygon around the feasible region based on the corner points identified on the graph. **System of Inequalities:** 1. \(2x + 5y \leq 30\) 2. \(4x + 5y \leq 40\) 3. \(x \geq 0\) 4. \(y \geq 0\) **Graph Details:** - The graph is a coordinate plane with \(x\) and \(y\) axes, extending from -2 to 10 on the x-axis and from 0 to 10 on the y-axis. - The inequalities will form boundary lines on the graph, and the area where all inequalities overlap will be shaded to show the feasible region. - The feasible region is the set of all points \((x, y)\) that satisfy all the given inequalities simultaneously. - Use the interactive graph tool to draw and adjust the polygon by selecting the corner points of the feasible region. **Instructions:** 1. Identify the critical points of intersection between the boundary lines. 2. Click on these points within the graph area to form a closed shape that represents the feasible region. 3. Once the polygon encloses the feasible region, click "Submit Question" to confirm your graph. This exercise demonstrates graphing systems of linear inequalities and visualizing solutions on a coordinate plane.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:### Graphing the Feasible Region for the System of Inequalities
To graph the feasible region for the following system of inequalities, draw a polygon around the feasible region based on the corner points identified on the graph.
**System of Inequalities:**
1. \(2x + 5y \leq 30\)
2. \(4x + 5y \leq 40\)
3. \(x \geq 0\)
4. \(y \geq 0\)
**Graph Details:**
- The graph is a coordinate plane with \(x\) and \(y\) axes, extending from -2 to 10 on the x-axis and from 0 to 10 on the y-axis.
- The inequalities will form boundary lines on the graph, and the area where all inequalities overlap will be shaded to show the feasible region.
- The feasible region is the set of all points \((x, y)\) that satisfy all the given inequalities simultaneously.
- Use the interactive graph tool to draw and adjust the polygon by selecting the corner points of the feasible region.
**Instructions:**
1. Identify the critical points of intersection between the boundary lines.
2. Click on these points within the graph area to form a closed shape that represents the feasible region.
3. Once the polygon encloses the feasible region, click "Submit Question" to confirm your graph.
This exercise demonstrates graphing systems of linear inequalities and visualizing solutions on a coordinate plane.
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