Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Sketch the region that corresponds to the given inequalities. 18x + 9y s 90 9x + 18y s 90 9x + 9ys 54 x 2 0, y 20 10 10 Solution Set Solution Set - -10 -5 10 10 10 -5 10 10 y 10 y 10 Solution Set Solution Set

Sketch the region that corresponds to the given inequalities. 18x + 9y s 90 9x + 18y s 90 9x + 9ys 54 x 2 0, y 20 10 10 Solution Set Solution Set - -10 -5 10 10 10 -5 10 10 y 10 y 10 Solution Set Solution Set

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
See similar textbooks
icon
Related questions
Question
**Title: Solving Inequalities through Graphical Interpretation** **Introduction:** This page demonstrates how to sketch regions corresponding to a set of inequalities using graphical methods. The inequalities given are: 1. \(18x + 9y \leq 90\) 2. \(9x + 18y \leq 90\) 3. \(9x + 9y \leq 54\) 4. \(x \geq 0\), \(y \geq 0\) **Graphical Representation:** The image contains four graphs each illustrating the solution set for the given system of inequalities. Each graph is displayed on the Cartesian coordinate system marked with axes \(x\) and \(y\). **Description of Graphs:** - **Graph Layout:** - Each graph has labeled axes with tick marks ranging approximately from -10 to 10. - The feasible region that satisfies all inequalities is shaded in blue. - Lines representing the boundary equations of each inequality are shown, dividing the plane into distinct regions. - **Feasible Solution Set:** - The area where all conditions of the inequalities are met (i.e., the "Solution Set") is highlighted. - This area represents all the possible values of \(x\) and \(y\) that satisfy the inequalities under given constraints (\(x \geq 0\), \(y \geq 0\)). By analyzing these graphs, one can visually interpret how different inequalities impose constraints and how they intersect to form the potential solution space. This method helps in understanding the behavior of the system and the range of solutions applicable under given conditions.
Transcribed Image Text:**Title: Solving Inequalities through Graphical Interpretation** **Introduction:** This page demonstrates how to sketch regions corresponding to a set of inequalities using graphical methods. The inequalities given are: 1. \(18x + 9y \leq 90\) 2. \(9x + 18y \leq 90\) 3. \(9x + 9y \leq 54\) 4. \(x \geq 0\), \(y \geq 0\) **Graphical Representation:** The image contains four graphs each illustrating the solution set for the given system of inequalities. Each graph is displayed on the Cartesian coordinate system marked with axes \(x\) and \(y\). **Description of Graphs:** - **Graph Layout:** - Each graph has labeled axes with tick marks ranging approximately from -10 to 10. - The feasible region that satisfies all inequalities is shaded in blue. - Lines representing the boundary equations of each inequality are shown, dividing the plane into distinct regions. - **Feasible Solution Set:** - The area where all conditions of the inequalities are met (i.e., the "Solution Set") is highlighted. - This area represents all the possible values of \(x\) and \(y\) that satisfy the inequalities under given constraints (\(x \geq 0\), \(y \geq 0\)). By analyzing these graphs, one can visually interpret how different inequalities impose constraints and how they intersect to form the potential solution space. This method helps in understanding the behavior of the system and the range of solutions applicable under given conditions.
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS