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Graph the feasible region for the given system of inequalities. x + 2y ≤ 8 2x + y ≤ 8 x ≥ 0 y 20 ... Use the graphing tool on the right to graph the system of inequalities. Click to enlarge graph 10 -8 -4 Ay 10- 8- 10 10

Graph the feasible region for the given system of inequalities. x + 2y ≤ 8 2x + y ≤ 8 x ≥ 0 y 20 ... Use the graphing tool on the right to graph the system of inequalities. Click to enlarge graph 10 -8 -4 Ay 10- 8- 10 10

Advanced Engineering Mathematics
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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### Graphing the Feasible Region for a System of Inequalities **System of Inequalities:** 1. \( x + 2y \leq 8 \) 2. \( 2x + y \leq 8 \) 3. \( x \geq 0 \) 4. \( y \geq 0 \) **Instructions:** Use the graphing tool on the right to plot the system of inequalities. **Graph Explanation:** - The graph is a coordinate plane with the x-axis and y-axis, each ranging from -10 to 10. - You are instructed to graph the feasible region for the given system of inequalities. - The x-axis and y-axis intersect at the origin (0,0). - The inequalities \( x \geq 0 \) and \( y \geq 0 \) mean the feasible region will be in the first quadrant, where both x and y are non-negative. ### How to Graph: 1. **Inequality 1: \( x + 2y \leq 8 \)** - Graph the line \( x + 2y = 8 \) first, then shade below this line. 2. **Inequality 2: \( 2x + y \leq 8 \)** - Graph the line \( 2x + y = 8 \) first, then shade below this line. 3. **Inequality 3 and 4:** - Since \( x \geq 0 \) and \( y \geq 0 \), shade the portion of the graph that is in the first quadrant. **Additional Features:** - The instructions mention a button "Click to enlarge graph," indicating that users on the website can view a larger version of the graphing tool for better visibility and interaction. This graphing activity helps in understanding the visual representation of solutions for a system of linear inequalities. The feasible region is the intersection area that satisfies all given inequalities.
Transcribed Image Text:### Graphing the Feasible Region for a System of Inequalities **System of Inequalities:** 1. \( x + 2y \leq 8 \) 2. \( 2x + y \leq 8 \) 3. \( x \geq 0 \) 4. \( y \geq 0 \) **Instructions:** Use the graphing tool on the right to plot the system of inequalities. **Graph Explanation:** - The graph is a coordinate plane with the x-axis and y-axis, each ranging from -10 to 10. - You are instructed to graph the feasible region for the given system of inequalities. - The x-axis and y-axis intersect at the origin (0,0). - The inequalities \( x \geq 0 \) and \( y \geq 0 \) mean the feasible region will be in the first quadrant, where both x and y are non-negative. ### How to Graph: 1. **Inequality 1: \( x + 2y \leq 8 \)** - Graph the line \( x + 2y = 8 \) first, then shade below this line. 2. **Inequality 2: \( 2x + y \leq 8 \)** - Graph the line \( 2x + y = 8 \) first, then shade below this line. 3. **Inequality 3 and 4:** - Since \( x \geq 0 \) and \( y \geq 0 \), shade the portion of the graph that is in the first quadrant. **Additional Features:** - The instructions mention a button "Click to enlarge graph," indicating that users on the website can view a larger version of the graphing tool for better visibility and interaction. This graphing activity helps in understanding the visual representation of solutions for a system of linear inequalities. The feasible region is the intersection area that satisfies all given inequalities.
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