Explanation Given information: The system of inequalities is, { 30 x + 10 y ≥ 50 10 x + 20 y ≥ 50 10 x _ 60 y ≥ 90 x ≥ 0 , y ≥ 0 Graph: The given system of inequalities can be rewrite as, 3 x + y ≥ 5 ...... (1) x + 2 y ≥ 5 ...... (2) x + 6 y ≥ 9 ...... (3) The corresponding equation of the inequality (1) is, 3 x + y = 5 Since, the inequality 3 x + y ≥ 5 involves the greater than or equal to sign, then the points on the line 3 x + y = 5 satisfies the inequality 3 x + y ≥ 5 . Therefore, the line 3 x + y = 5 itself is the part of the solution set. The corresponding equation of the inequality (2) is, x + 2 y ≥ 5 Since, the inequality x + 2 y ≥ 5 involves the greater than or equal to sign, then the points on the line x + 2 y = 5 satisfies the inequality x + 2 y ≥ 5 . Therefore, the line x + 2 y = 5 itself is the part of the solution set. The corresponding equation of the inequality (3) is, x + 6 y = 9 Since, the inequality x + 6 y ≥ 9 involves the greater than or equal to sign, then the points on the line x + 6 y = 9 satisfies the inequality x + 6 y ≥ 9 . Therefore, the line x + 6 y = 9 itself is the part of the solution set. Consider the test point ( 1 , 3 ) to check whether the solution satisfies each inequality of the given system. Substitute 1 for x and 3 for y in the inequality 3 x + y ≥ 5 . 3 x + y ≥ ? 5 3 ( 1 ) + 3 ≥ ? 5 3 + 3 ≥ ? 5 6 ≥ 5 The point ( 1 , 3 ) lies on the right side of the line 3 x + y = 5 and satisfies the inequality 3 x + y ≥ 5 . So it is the part of the solution set. Substitute 1 for x and 3 for y in the inequality x + 2 y ≥ 5 . x + 2 y ≥ ? 5 1 + 2 ( 3 ) ≥ ? 5 1 + 6 ≥ ? 5 7 ≥ 5 The point ( 1 , 3 ) lies on the right side of the line x + 2 y = 5 and satisfies the inequality x + 2 y ≥ 5 . So it is the part of the solution set. Substitute 1 for x and 3 for y in the inequality x + 6 y ≥ 9 . x + 6 y ≥ ? 9 1 + 6 ( 3 ) ≥ ? 9 1 + 18 ≥ ? 9 19 ≥ 9 The point ( 1 , 3 ) lies on the right side of the line x + 6 y = 9 and satisfies the inequality x + 6 y ≥ 9 . So it is the part of the solution set. Therefore, the test point ( 1 , 3 ) satisfies each inequality of the given system. The solution set of the given system of inequalities is the intersection of the solutions of each of the given inequality. Therefore, the solution set is shown as shaded region in Figure 1. The vertices occur at the points of intersection of the corresponding equation of the given system of inequalities. 3 x + y = 5 ...... (4) x + 2 y = 5

Bundle: College Algebra, 7th + WebAssign Printed Access Card for Stewart/Redlin/Watson's College Algebra, 7th Edition, Single-Term

7th Edition

ISBN: 9781305718944

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 5.5, Problem 63E

To determine

To graph:

The system of inequality {30x+10y≥5010x+20y≥5010x_60y≥90x≥0,y≥0. Also find the coordinates of all vertices, and check whether the solution set is bounded or unbounded.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 5.5, Problem 62E

Chapter 5.5, Problem 64E

Students have asked these similar questions

Directions: Use the table below to answer the following questions and show all work. Heights of Females 50.0 51.5 53.0 53.5 54.0 1. What is the average female height? 2. What are all the differences from the mean? 3. What is the variance for the female heights? 4. What is the standard deviation of the heights of the females? 5. What does the standard deviation found in number 4 represent? Write your answer in complete sentences.

135 metr uzunlikdagi simni 6:3 nisbatda qismlarga am eating

In circle T with m, angle, S, T, U, equals, 168, degreesm∠STU=168∘ and S, T, equals, 12ST=12, find the area of sector STU. Round to the nearest hundredth.

Chapter 5 Solutions

Bundle: College Algebra, 7th + WebAssign Printed Access Card for Stewart/Redlin/Watson's College Algebra, 7th Edition, Single-Term

Ch. 5.1 - The system of equations {2x+3y=75xy=9} is a system...Ch. 5.1 - A system of equation in two variable can be solved...Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Elimination method Use the elimination method to...Ch. 5.1 - Elimination method Use the elimination method to...Ch. 5.1 - Elimination method Use the elimination method to...Ch. 5.1 - Elimination method Use the elimination method to...Ch. 5.1 - Elimination method Use the elimination method to...Ch. 5.1 - Elimination method Use the elimination method to...

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

To graph: The system of inequality { 30 x + 10 y ≥ 50 10 x + 20 y ≥ 50 10 x _ 60 y ≥ 90 x ≥ 0 , y ≥ 0 . Also find the coordinates of all vertices, and check whether the solution set is bounded or unbounded.

Solution Summary: The author explains how the given system of inequalities can be rewritten as 3x+yge 5.

Videos

To graph:

The system of inequality {30x+10y≥5010x+20y≥5010x_60y≥90x≥0,y≥0. Also find the coordinates of all vertices, and check whether the solution set is bounded or unbounded.

Want to see the full answer?

Chapter 5 Solutions

To graph: The system of inequality { 30 x + 10 y ≥ 50 10 x + 20 y ≥ 50 10 x _ 60 y ≥ 90 x ≥ 0 , y ≥ 0 . Also find the coordinates of all vertices, and check whether the solution set is bounded or unbounded.

Solution Summary: The author explains how the given system of inequalities can be rewritten as 3x+yge 5.

Videos

To graph: The system of inequality {30x+10y≥5010x+20y≥5010x_60y≥90x≥0,y≥0. Also find the coordinates of all vertices, and check whether the solution set is bounded or unbounded.

Want to see the full answer?

Chapter 5 Solutions

To graph:

The system of inequality {30x+10y≥5010x+20y≥5010x_60y≥90x≥0,y≥0. Also find the coordinates of all vertices, and check whether the solution set is bounded or unbounded.