Graph the feasible region for the follow system of inequalities by drawing a polygon around the feasible region. Click to set the corner points. 9 2+y 5x + 6y > 45 x + y x + y 0 0 10+ ε X Y -2 -1 ∞ \ Φ 3 2 1 -1 -2 ΛΙ ΛΙ ΛΙ VI ΛΙΛΙ 1 2 3 4 5 6 7 8 9 10
Graph the feasible region for the follow system of inequalities by drawing a polygon around the feasible region. Click to set the corner points. 9 2+y 5x + 6y > 45 x + y x + y 0 0 10+ ε X Y -2 -1 ∞ \ Φ 3 2 1 -1 -2 ΛΙ ΛΙ ΛΙ VI ΛΙΛΙ 1 2 3 4 5 6 7 8 9 10
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 Feasible Regions by Inequalities
## Problem Description
Graph the feasible region for the following system of inequalities by drawing a polygon around the feasible region. Click to set the corner points.
\[
\begin{cases}
2x + y \geq 9 \\
5x + 6y \geq 45 \\
x + y \geq 8 \\
x + y \leq 9 \\
x \geq 0 \\
y \geq 0 \\
\end{cases}
\]
## Coordinate Plane Description
The provided coordinate plane has a grid that extends from -2 to 10 on both the x and y axes. The region to be graphed will take into account the constraints provided by the inequalities.
### Graph and Interpret the Inequalities
1. **First Inequality: \(2x + y \geq 9\)**
- This inequality represents a region above the line \(2x + y = 9\).
2. **Second Inequality: \(5x + 6y \geq 45\)**
- This inequality represents a region above the line \(5x + 6y = 45\).
3. **Third Inequality: \(x + y \geq 8\)**
- This inequality represents a region above the line \(x + y = 8\).
4. **Fourth Inequality: \(x + y \leq 9\)**
- This inequality represents a region below the line \(x + y = 9\).
5. **Fifth Inequality: \(x \geq 0\)**
- This inequality represents the region to the right of the y-axis.
6. **Sixth Inequality: \(y \geq 0\)**
- This inequality represents the region above the x-axis.
By plotting these inequalities on the coordinate plane and shading the appropriate regions, we identify and mark the polygon representing the feasible region. This polygon is formed by the intersection of all the lines obeying the inequalities, typically with the boundary lines included.
**Corner Points:**
The corner points of the feasible region can be found at the intersection points of the boundary lines, satisfying all the inequalities.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53b99f33-5097-48ca-9202-113ad6b052b9%2F87460693-6c40-4161-a7d0-63859dfa56ff%2F4gfklop_processed.png&w=3840&q=75)
Transcribed Image Text:# Graphing Feasible Regions by Inequalities
## Problem Description
Graph the feasible region for the following system of inequalities by drawing a polygon around the feasible region. Click to set the corner points.
\[
\begin{cases}
2x + y \geq 9 \\
5x + 6y \geq 45 \\
x + y \geq 8 \\
x + y \leq 9 \\
x \geq 0 \\
y \geq 0 \\
\end{cases}
\]
## Coordinate Plane Description
The provided coordinate plane has a grid that extends from -2 to 10 on both the x and y axes. The region to be graphed will take into account the constraints provided by the inequalities.
### Graph and Interpret the Inequalities
1. **First Inequality: \(2x + y \geq 9\)**
- This inequality represents a region above the line \(2x + y = 9\).
2. **Second Inequality: \(5x + 6y \geq 45\)**
- This inequality represents a region above the line \(5x + 6y = 45\).
3. **Third Inequality: \(x + y \geq 8\)**
- This inequality represents a region above the line \(x + y = 8\).
4. **Fourth Inequality: \(x + y \leq 9\)**
- This inequality represents a region below the line \(x + y = 9\).
5. **Fifth Inequality: \(x \geq 0\)**
- This inequality represents the region to the right of the y-axis.
6. **Sixth Inequality: \(y \geq 0\)**
- This inequality represents the region above the x-axis.
By plotting these inequalities on the coordinate plane and shading the appropriate regions, we identify and mark the polygon representing the feasible region. This polygon is formed by the intersection of all the lines obeying the inequalities, typically with the boundary lines included.
**Corner Points:**
The corner points of the feasible region can be found at the intersection points of the boundary lines, satisfying all the inequalities.
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