Homework Help is Here – Start Your Trial Now!
Math
Algebra
Graph the feasible region for the follow system of inequalities by drawing a polygon around the feasible x + y <8 -x+y > 3 > 1 region. Click to set the corner points. + 8 + 7 6 5 4 3 2 1 -1+ 1 2 3 5 6 X 8

Graph the feasible region for the follow system of inequalities by drawing a polygon around the feasible x + y <8 -x+y > 3 > 1 region. Click to set the corner points. + 8 + 7 6 5 4 3 2 1 -1+ 1 2 3 5 6 X 8

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
See similar textbooks
icon
Related questions
Question
### Graphing Linear Inequalities: Feasible Region To understand how to graph the feasible region for a system of linear inequalities, we will analyze an example system and illustrate it on a Cartesian plane. Below is a system of inequalities and an empty graph where we can plot these inequalities to visualize the feasible region. #### System of Inequalities \[ \begin{cases} x + y \leq 8 \\ -x + y \geq 3 \\ x \geq 1 \end{cases} \] ### Steps for Graphing 1. **Graph each inequality separately**: - **Equation 1: \(x + y \leq 8\)** - Convert the inequality into an equation: \(x + y = 8\). - Find the intercepts: - When \(x = 0\), \(y = 8\) (point \((0,8)\)). - When \(y = 0\), \(x = 8\) (point \((8,0)\)). - Draw the line through these points. - Shade the area below this line (since \(y\) is less than or equal to the expression \(8 - x\)). - **Equation 2: \(-x + y \geq 3\)** - Convert the inequality into an equation: \(-x + y = 3\). - Find the intercepts: - When \(x = 0\), \(y = 3\) (point \((0,3)\)). - When \(y = 0\), \(x = -3\) (point \((-3,0)\)). - Draw the line through these points. - Shade the area above this line (since \(y\) is greater than or equal to the expression \(3 + x\)). - **Equation 3: \(x \geq 1\)** - This inequality represents a vertical line at \(x = 1\). - Draw the vertical line passing through \(x = 1\). - Shade the area to the right of this line (since \(x\) is greater than or equal to 1). 2. **Identify the Feasible Region**: - The feasible region is where all shaded areas intersect. To draw the polygon around
Transcribed Image Text:### Graphing Linear Inequalities: Feasible Region To understand how to graph the feasible region for a system of linear inequalities, we will analyze an example system and illustrate it on a Cartesian plane. Below is a system of inequalities and an empty graph where we can plot these inequalities to visualize the feasible region. #### System of Inequalities \[ \begin{cases} x + y \leq 8 \\ -x + y \geq 3 \\ x \geq 1 \end{cases} \] ### Steps for Graphing 1. **Graph each inequality separately**: - **Equation 1: \(x + y \leq 8\)** - Convert the inequality into an equation: \(x + y = 8\). - Find the intercepts: - When \(x = 0\), \(y = 8\) (point \((0,8)\)). - When \(y = 0\), \(x = 8\) (point \((8,0)\)). - Draw the line through these points. - Shade the area below this line (since \(y\) is less than or equal to the expression \(8 - x\)). - **Equation 2: \(-x + y \geq 3\)** - Convert the inequality into an equation: \(-x + y = 3\). - Find the intercepts: - When \(x = 0\), \(y = 3\) (point \((0,3)\)). - When \(y = 0\), \(x = -3\) (point \((-3,0)\)). - Draw the line through these points. - Shade the area above this line (since \(y\) is greater than or equal to the expression \(3 + x\)). - **Equation 3: \(x \geq 1\)** - This inequality represents a vertical line at \(x = 1\). - Draw the vertical line passing through \(x = 1\). - Shade the area to the right of this line (since \(x\) is greater than or equal to 1). 2. **Identify the Feasible Region**: - The feasible region is where all shaded areas intersect. To draw the polygon around
Expert Solution
steps

Step by step

Solved in 3 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS