Explanation Given Information: The provided inequalities are, x + 2 y ≥ 10 2 x + y ≥ 11 x + y ≥ 9 x ≥ 0 , y ≥ 0 Graph: Consider the provided system of inequalities, x + 2 y ≥ 10 2 x + y ≥ 11 x + y ≥ 9 x ≥ 0 , y ≥ 0 To find the region for inequality x + 2 y ≥ 10 . First calculate the intercepts points of line x + 2 y = 10 . Now, put y = 0 to calculate the x -intercept of the equation x + 2 y = 10 . So, x + 2 ( 0 ) = 10 x = 10 Now, put x = 0 to calculate the y -intercept of the equation x + 2 y = 10 . So, 0 + 2 y = 10 2 y = 10 y = 5 Therefore the intercept points of the line x + 2 y = 10 are ( 10 , 0 ) and ( 0 , 5 ) . So, graph x + 2 y = 10 as a solid line. The solution region for inequality x + 2 y ≥ 10 is the half plane that contains the point for which the sum of x + 2 y is greater than or equal to 10. To find the region for inequality 2 x + y ≥ 11 . First calculate the intercepts points of line 2 x + y = 11 . Now, put y = 0 to calculate the x -intercept of the equation 2 x + y = 11 . So, 2 x + 0 = 11 x = 11 2 Now, put x = 0 to calculate the y -intercept of the equation 2 x + y = 11 . So, 2 ( 0 ) + y = 11 y = 11 Therefore the intercept points of the line 2 x + y = 11 are ( 11 2 , 0 ) and ( 0 , 11 ) . So, graph 2 x + y = 11 as a solid line. The solution region for inequality 2 x + y ≥ 11 is the half plane that contains the point for which the term 2 x + y is greater than or equal to 11. To find the region for inequality x + y ≥ 9 . First calculate the intercepts points of line x + y = 9 . Now, put y = 0 to calculate the x -intercept of the equation x + y = 9 . So, x + 0 = 9 x = 9 Now, put x = 0 to calculate the y -intercept of the equation x + y = 9 . So, 0 + y = 9 y = 9 Therefore the intercept points of the line x + y ≥ 9 are ( 9 , 0 ) and ( 0 , 9 ) . So, graph 2 x + y = 50 as a solid line. The solution region for inequality x + y = 9 is the half plane that contains the point for which the term x + y is greater than or equal to 9. Now, to find the common shaded region consider any test point say ( 6 , 6 ) . For first inequality x + 2 y ≥ 10 , Substitute 6 for x and 6 for y in provided inequality. 6 + 2 ( 6 ) ≥ 10 18 ≥ 10 This is correct. For second inequality 2 x + y ≥ 11 , Substitute 6 for x and 6 for y in provided inequality

Mathematical Applications for the Management, Life, and Social Sciences

12th Edition

ISBN: 9781337625340

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 4.1, Problem 24E

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To graph: The solution of the system of inequalities,

x+2y≥102x+y≥11x+y≥9x≥0,y≥0

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Chapter 4.1, Problem 23E

Chapter 4.1, Problem 25E

Chapter 4 Solutions

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To graph: The solution of the system of inequalities, x + 2 y ≥ 10 2 x + y ≥ 11 x + y ≥ 9 x ≥ 0 , y ≥ 0

Solution Summary: The author analyzes the solution of the system of inequalities, cx+2y

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To graph: The solution of the system of inequalities,

x+2y≥102x+y≥11x+y≥9x≥0,y≥0

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Chapter 4 Solutions

To graph: The solution of the system of inequalities, x + 2 y ≥ 10 2 x + y ≥ 11 x + y ≥ 9 x ≥ 0 , y ≥ 0

Solution Summary: The author analyzes the solution of the system of inequalities, cx+2y

Videos

To graph: The solution of the system of inequalities, x+2y≥102x+y≥11x+y≥9x≥0,y≥0

Want to see the full answer?

Chapter 4 Solutions

To graph: The solution of the system of inequalities,

x+2y≥102x+y≥11x+y≥9x≥0,y≥0