Explanation The given linear inequalities are as follows, 3 x + 4 y > 12 (1) 2 x − 3 y < 6 (2) 0 ≤ y ≤ 2 (3) Consider the equation (1). The inequality in the given equation is >. Therefore, the dashed line is used to join the coordinates of this equation. Now, replace the inequality symbol in the given equation 3 x + 4 y > 12 with “equals” symbol. Then the equation (1) becomes, 3 x + 4 y = 12 . Obtain any 2 points of the above equation to plot on the line. Consider x = 0 , 4 and obtain the corresponding values of y respectively. Substitute x = 0 in the linear equation 3 x + 4 y = 12 , 3 ( 0 ) + 4 y = 12 4 y = 12 y = 12 4 y = 3 Thus, the value of y is 3 at x = 0 . Hence, the first coordinate is ( 0 , 3 ) . Substitute x = 4 in the linear equation 3 x + 4 y = 12 . 3 ( 4 ) + 4 y = 12 12 + 4 y = 12 4 y = 12 − 12 y = 0 Thus, the value of y is 0 at x = 4 . Hence, the second coordinate is ( 4 , 0 ) . Therefore, the coordinates are ( 0 , 3 ) and ( 4 , 0 ) . Now determine whether the statement is true or false using test point. Let the test point be ( 0 , 0 ) . Now substitute the test point ( 0 , 0 ) in 3 x + 4 y > 12 . 3 ( 0 ) + 4 ( 0 ) > 12 0 > 12 It is noticed that the inequality 3 x + 4 y = 12 is false. Thus, shade the half-plane that does not contain the test point ( 0 , 0 ) . That is the half-plane above the line. Consider the equation (2), The inequality in the given equation is <. Therefore, the dashed line is used to join the coordinates of this equation. Now, replace the inequality symbol in the given equation 2 x − 3 y < 6 with “equals” symbol. Then the equation (2) becomes, 2 x − 3 y = 6 . Obtain any 2 points of the above equation to plot on the line. Consider x = 0 , 3 and obtain the corresponding values of y respectively. Substitute x = 0 in the linear equation 2 x − 3 y = 6 , 2 ( 0 ) − 3 y = 6 − 3 y = 6 y = − 6 3 y = − 2 Thus, the value of y is − 2 at x = 0 . Hence, the first coordinate is ( 0 , − 2 ) . Substitute x = 3 in the linear equation 2 x − 3 y = 6 . 2 ( 3 ) − 3 y = 6 6 − 3 y = 6 − 3 y = 6 − 6 y = 0 Thus, the value of y is 0 at x = 3

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Chapter 3.1, Problem 31E

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To sketch: The graph of the feasible region for the system of inequalities 3x+4y>12 , 2x−3y<6 , 0≤y≤2 ; x≥0 and check whether the region is bounded or unbounded.

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Chapter 3.1, Problem 30E

Chapter 3.1, Problem 32E

Chapter 3 Solutions

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Ch. 3.1 - Graph 3x + 2y 18.Ch. 3.1 - Graph the feasible region for the system...Ch. 3.1 - Prob. 1WE Ch. 3.1 - y=12x+1 Ch. 3.1 - Prob. 3WE Ch. 3.1 - Prob. 4WE Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E

Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Graph the feasible region for each system of...Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Graph the feasible region for each system of...Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - The regions A through G in the figure can be...Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - For Exercises 4247, perform the following steps....Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - For Exercises 4247, perform the following steps....Ch. 3.1 - Prob. 47E Ch. 3.2 - Prob. 1YT Ch. 3.2 - Prob. 1WE Ch. 3.2 - Prob. 2WE Ch. 3.2 - Prob. 3WE Ch. 3.2 - Prob. 4WE Ch. 3.2 - Prob. 1E Ch. 3.2 - Prob. 2E Ch. 3.2 - Prob. 3E Ch. 3.2 - Prob. 4E Ch. 3.2 - Prob. 5E Ch. 3.2 - Prob. 6E Ch. 3.2 - Prob. 7E Ch. 3.2 - Prob. 8E Ch. 3.2 - Prob. 9E Ch. 3.2 - Prob. 10E Ch. 3.2 - Prob. 11E Ch. 3.2 - Prob. 12E Ch. 3.2 - Prob. 13E Ch. 3.2 - Prob. 14E Ch. 3.2 - Prob. 15E Ch. 3.2 - Prob. 16E Ch. 3.2 - Prob. 17E Ch. 3.3 - Prob. 1YT Ch. 3.3 - Prob. 2YT Ch. 3.3 - Prob. 3YT Ch. 3.3 - Prob. 1WE Ch. 3.3 - Prob. 2WE Ch. 3.3 - Prob. 1E Ch. 3.3 - Prob. 2E Ch. 3.3 - Prob. 3E Ch. 3.3 - Prob. 4E Ch. 3.3 - Prob. 5E Ch. 3.3 - Prob. 6E Ch. 3.3 - Prob. 7E Ch. 3.3 - Prob. 8E Ch. 3.3 - Finance A pension fund manager decides to invest a...Ch. 3.3 - Prob. 10E Ch. 3.3 - Prob. 11E Ch. 3.3 - Prob. 12E Ch. 3.3 - Blending The Mostpure Milk Company gets milk from...Ch. 3.3 - Profit The Muro Manufacturing Company makes two...Ch. 3.3 - Revenue A machine shop manufactures two types of...Ch. 3.3 - Revenue The manufacturing process requires that...Ch. 3.3 - Transportation A flash drive manufacturer has 370...Ch. 3.3 - Prob. 18E Ch. 3.3 - Prob. 19E Ch. 3.3 - Prob. 20E Ch. 3.3 - Life Sciences 21. Health Care David Willis takes...Ch. 3.3 - Predator Food Requirements A certain predator...Ch. 3.3 - Nutrition A dietician is planning a snack package...Ch. 3.3 - Health Care Jennifer Morales was given the...Ch. 3.3 - Prob. 25E Ch. 3.3 - Prob. 26E Ch. 3 - Determine whether each of the following statements...Ch. 3 - Determine whether each of the following statements...Ch. 3 - Determine whether each of the following statements...Ch. 3 - Prob. 4RE Ch. 3 - Determine whether each of the following statements...Ch. 3 - Prob. 6RE Ch. 3 - Determine whether each of the following statements...Ch. 3 - Prob. 8RE Ch. 3 - Determine whether each of the following statements...Ch. 3 - Prob. 10RE Ch. 3 - Determine whether each of the following statements...Ch. 3 - Prob. 12RE Ch. 3 - Determine whether each of the following statements...Ch. 3 - Prob. 14RE Ch. 3 - Graph each linear inequality. 15. y 2x + 3 Ch. 3 - Prob. 16RE Ch. 3 - Graph each linear inequality. 17. 2x + 6y 8 Ch. 3 - Prob. 18RE Ch. 3 - Graph each linear inequality. 19. y x Ch. 3 - Prob. 20RE Ch. 3 - Graph the solution of each system of inequalities....Ch. 3 - Prob. 22RE Ch. 3 - Graph the solution of each system of inequalities....Ch. 3 - Prob. 24RE Ch. 3 - Graph the solution of each system of inequalities....Ch. 3 - Prob. 26RE Ch. 3 - Use the given regions to find the maximum and...Ch. 3 - Prob. 28RE Ch. 3 - Use the graphical method to solve each linear...Ch. 3 - Prob. 30RE Ch. 3 - Use the graphical method to solve each linear...Ch. 3 - Prob. 32RE Ch. 3 - Prob. 33RE Ch. 3 - Prob. 34RE Ch. 3 - It is not necessary to check all corner points in...Ch. 3 - Prob. 36RE Ch. 3 - Prob. 37RE Ch. 3 - Prob. 38RE Ch. 3 - Profit Refer to Exercise 37. (a) How many batches...Ch. 3 - Prob. 40RE Ch. 3 - Prob. 41RE Ch. 3 - Construction A contractor builds boathouses in two...Ch. 3 - Prob. 43RE Ch. 3 - Prob. 44RE Ch. 3 - Prob. 45RE Ch. 3 - General Interest 46. Studying Ty Olden is trying...

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The graph of the feasible region for the system of inequalities 3 x + 4 y > 12 , 2 x − 3 y < 6 , 0 ≤ y ≤ 2 ; x ≥ 0 and check whether the region is bounded or unbounded.

Solution Summary: The author explains the feasible region for the system of inequalities. The dashed line is used to join the coordinates of the equation.

Videos

To sketch: The graph of the feasible region for the system of inequalities 3x+4y>12 , 2x−3y<6 , 0≤y≤2 ; x≥0 and check whether the region is bounded or unbounded.

Want to see the full answer?

Chapter 3 Solutions

The graph of the feasible region for the system of inequalities 3 x + 4 y &gt; 12 , 2 x − 3 y &lt; 6 , 0 ≤ y ≤ 2 ; x ≥ 0 and check whether the region is bounded or unbounded.

Solution Summary: The author explains the feasible region for the system of inequalities. The dashed line is used to join the coordinates of the equation.

Videos

To sketch: The graph of the feasible region for the system of inequalities 3x+4y>12 , 2x−3y<6 , 0≤y≤2 ; x≥0 and check whether the region is bounded or unbounded.

Want to see the full answer?

Chapter 3 Solutions

The graph of the feasible region for the system of inequalities 3 x + 4 y > 12 , 2 x − 3 y < 6 , 0 ≤ y ≤ 2 ; x ≥ 0 and check whether the region is bounded or unbounded.