Explanation Given Information: The inequalities: x + 2 y ≥ 19 3 x + 2 y ≥ 29 x ≥ 0 , y ≥ 0 Graph: Consider the provided system of inequalities. x + 2 y ≥ 19 3 x + 2 y ≥ 29 x ≥ 0 , y ≥ 0 To find the region for inequality x + 2 y ≥ 19 . First calculate the intercepts points of line x + 2 y = 19 . Now, put y = 0 to calculate the x -intercept of the equation x + 2 y = 19 . So, x + 2 ( 0 ) = 19 x = 19 Now, put x = 0 to calculate the y -intercept of the equation x + 2 y = 19 . So, 0 + 2 y = 19 2 y = 19 y = 19 2 Therefore the intercept points of the line x + 2 y = 19 are ( 19 , 0 ) and ( 0 , 19 2 ) . So, graph x + 2 y = 19 as a solid line. The solution region for inequality x + 2 y ≥ 19 is the half plane that contains the point for which the sum of x + 2 y is greater than or equal to 19. To find the region for inequality 3 x + 2 y ≥ 29 . First calculate the intercepts points of line 3 x + 2 y = 29 . Now, put y = 0 to calculate the x -intercept of the equation 3 x + 2 y = 29 . So, 3 x + 2 ( 0 ) = 29 3 x = 29 x = 29 3 Now, put x = 0 to calculate the y -intercept of the equation 3 x + 2 y = 29 . So, 3 ( 0 ) + 2 y = 29 2 y = 29 y = 29 2 Therefore the intercept points of the line 3 x + 2 y = 29 are ( 29 3 , 0 ) and ( 0 , 29 2 ) . So, graph 3 x + 2 y = 29 as a solid line. The solution region for inequality 3 x + 2 y ≥ 29 is the half plane that contains the point for which the term 3 x + 2 y is greater than or equal to 29. Now, to find the common shaded region consider any test point say ( 10 , 10 ) . For first inequality x + 2 y ≥ 19 , Substitute 10 for x and 10 for y in provided inequality. ( 10 ) + 2 ( 10 ) ≥ 19 30 ≥ 19 This is correct

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 21E

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To graph: The solution of the system of inequalities:

x+2y≥193x+2y≥29x≥0,y≥0

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Chapter 4.1, Problem 20E

Chapter 4.1, Problem 22E

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To graph: The solution of the system of inequalities: x + 2 y ≥ 19 3 x + 2 y ≥ 29 x ≥ 0 , y ≥ 0

Solution Summary: The author explains how to graph the solution of the system of inequalities.

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To graph: The solution of the system of inequalities:

x+2y≥193x+2y≥29x≥0,y≥0

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Chapter 4 Solutions

To graph: The solution of the system of inequalities: x + 2 y ≥ 19 3 x + 2 y ≥ 29 x ≥ 0 , y ≥ 0

Solution Summary: The author explains how to graph the solution of the system of inequalities.

Videos

To graph: The solution of the system of inequalities: x+2y≥193x+2y≥29x≥0,y≥0

Want to see the full answer?

Chapter 4 Solutions

To graph: The solution of the system of inequalities:

x+2y≥193x+2y≥29x≥0,y≥0