Graph the following system of linear inequalities. x+ 2y < 16 2x + y< 24 x20 y 20
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Graph the following system of linear inequalities.
\[
\begin{align*}
x + 2y &\leq 16 \\
2x + y &\leq 24 \\
x &\geq 0 \\
y &\geq 0 \\
\end{align*}
\]
**Explanation for Graph:**
- The graph represents a system of linear inequalities.
- The inequality \(x + 2y \leq 16\) is depicted by a line with a shaded region below it, showing all the points \((x, y)\) that satisfy the condition.
- The inequality \(2x + y \leq 24\) is represented by another line, with its own shaded region below it.
- The \(x \geq 0\) and \(y \geq 0\) inequalities indicate that only points in the first quadrant (where both x and y are non-negative) are considered.
- The solution to the system is the overlapping area of all these regions, often called the feasible region.
Understanding and analyzing these inequalities graphically helps in visualizing the feasible solutions satisfying all given conditions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd920f800-7cb4-4708-a86f-fdc64006663e%2Fec4476bb-529d-4038-ba4b-e41da2389447%2Fjhosco_processed.png&w=3840&q=75)
Transcribed Image Text:Graph the following system of linear inequalities.
\[
\begin{align*}
x + 2y &\leq 16 \\
2x + y &\leq 24 \\
x &\geq 0 \\
y &\geq 0 \\
\end{align*}
\]
**Explanation for Graph:**
- The graph represents a system of linear inequalities.
- The inequality \(x + 2y \leq 16\) is depicted by a line with a shaded region below it, showing all the points \((x, y)\) that satisfy the condition.
- The inequality \(2x + y \leq 24\) is represented by another line, with its own shaded region below it.
- The \(x \geq 0\) and \(y \geq 0\) inequalities indicate that only points in the first quadrant (where both x and y are non-negative) are considered.
- The solution to the system is the overlapping area of all these regions, often called the feasible region.
Understanding and analyzing these inequalities graphically helps in visualizing the feasible solutions satisfying all given conditions.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
