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Graph the feasible region for the given system of inequalities. x + 3y ≤ 9 3x + y ≤ 9 x 20 y20

Graph the feasible region for the given system of inequalities. x + 3y ≤ 9 3x + y ≤ 9 x 20 y20

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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**Question 30 of 40** **Graph the feasible region for the given system of inequalities:** - \( x + 3y \leq 9 \) - \( 3x + y \leq 9 \) - \( x \geq 0 \) - \( y \geq 0 \) **Instructions:** Use the graphing tool on the right to graph the system of inequalities. *Click to enlarge graph* --- **Graph Details:** The graph is a coordinate grid with the x-axis labeled from -10 to 10 and the y-axis labeled from -10 to 10. Each axis is marked with grid lines at each integer point. The graphing tool allows you to plot the inequalities and shade the region that satisfies all inequalities. - **\( x + 3y \leq 9 \):** This inequality represents a line that crosses the x-axis at \( (9, 0) \) and the y-axis at \( (0, 3) \). The area below this line is included. - **\( 3x + y \leq 9 \):** This inequality's line crosses the x-axis at \( (3, 0) \) and the y-axis at \( (0, 9) \). The area below this line is also included. - **\( x \geq 0 \):** This inequality includes all points on and to the right of the y-axis. - **\( y \geq 0 \):** This inequality includes all points on and above the x-axis. The feasible region is the intersection of all shaded areas on the graph, forming a bounded area in the first quadrant. **Navigation:** - Use zoom buttons to adjust the view. - Enlarge the graph by clicking on the appropriate button to explore details. --- **Quiz Navigation:** - **This quiz:** 40 point(s) possible - **This question:** 1 point(s) possible *Options: Resume later, Submit quiz*
Transcribed Image Text:**Question 30 of 40** **Graph the feasible region for the given system of inequalities:** - \( x + 3y \leq 9 \) - \( 3x + y \leq 9 \) - \( x \geq 0 \) - \( y \geq 0 \) **Instructions:** Use the graphing tool on the right to graph the system of inequalities. *Click to enlarge graph* --- **Graph Details:** The graph is a coordinate grid with the x-axis labeled from -10 to 10 and the y-axis labeled from -10 to 10. Each axis is marked with grid lines at each integer point. The graphing tool allows you to plot the inequalities and shade the region that satisfies all inequalities. - **\( x + 3y \leq 9 \):** This inequality represents a line that crosses the x-axis at \( (9, 0) \) and the y-axis at \( (0, 3) \). The area below this line is included. - **\( 3x + y \leq 9 \):** This inequality's line crosses the x-axis at \( (3, 0) \) and the y-axis at \( (0, 9) \). The area below this line is also included. - **\( x \geq 0 \):** This inequality includes all points on and to the right of the y-axis. - **\( y \geq 0 \):** This inequality includes all points on and above the x-axis. The feasible region is the intersection of all shaded areas on the graph, forming a bounded area in the first quadrant. **Navigation:** - Use zoom buttons to adjust the view. - Enlarge the graph by clicking on the appropriate button to explore details. --- **Quiz Navigation:** - **This quiz:** 40 point(s) possible - **This question:** 1 point(s) possible *Options: Resume later, Submit quiz*
Expert Solution
Step 1

Given a system of inequality are as follows:

x+3y≤93a+y≤9x≥0y≥0

To Plot: The graph of the feasible region for the given system of inequality.

 

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