Explanation Given: Maximize z = 10 x + 8 y . Subject to: 2 x + 3 y ≤ 100 5 x + 4 y ≤ 200 x ≥ 10 0 ≤ y ≤ 20 Calculation: The given linear inequalities are as follows, 2 x + 3 y ≤ 100 (1) 5 x + 4 y ≤ 200 (2) x ≥ 10 (3) 0 ≤ y ≤ 20 (4) Consider the equation (1). The given inequality in the equation is ≤ . Therefore, the solid line is used to join the coordinates of this equation. Now, replace the inequality symbol in the given equation 2 x + 3 y ≤ 100 with “equal to” symbol. Then the equation (1) becomes, 2 x + 3 y = 100 . Obtain any 2 points of the above equation to plot on the line. Consider x = 0 , 50 and obtain the corresponding values of y respectively. Substitute x = 0 in the linear equation 2 x + 3 y = 100 . 2 ( 0 ) + 3 y = 100 3 y = 100 y = 100 3 Thus, the value of y is 100 3 at x = 0 . Hence, the first coordinate is ( 0 , 100 3 ) . Substitute x = 50 in the linear equation 2 x + 3 y = 100 . 2 ( 50 ) + 3 y = 100 100 + 3 y = 100 3 y = 100 − 100 y = 0 Thus, the value of y is 0 at x = 50 . Hence, the second coordinate is ( 50 , 0 ) . Therefore, the coordinates are ( 0 , 100 3 ) and ( 50 , 0 ) . Now determine whether the inequality is true or false using test point. Let the test point be ( 0 , 0 ) . Now substitute the test point ( 0 , 0 ) in 2 x + 3 y ≤ 100 . 2 ( 0 ) + 3 ( 0 ) ≤ 100 0 ≤ 100 It is noticed that the inequality 2 x + 3 y ≤ 100 is true. Thus, shade the half-plane that contain the test point ( 0 , 0 ) . That is, the half-plane below the line. Consider the equation (2). The given inequality in the equation is ≤ . Therefore, the solid line is used to join the coordinates of this equation. Now, replace the inequality symbol in the given equation 5 x + 4 y ≤ 200 with “equals” symbol. Then the equation (2) becomes, 5 x + 4 y = 200 . Obtain any 2 points of the above equation to plot on the line. Consider x = 0 , 40 and obtain the corresponding values of y respectively. Substitute x = 0 in the linear equation 5 x + 4 y = 200 . 5 ( 0 ) + 4 y = 200 4 y = 200 y = 200 4 y = 50 Thus, the value of y is 50 at x = 0 . Hence, the first coordinate is ( 0 , 50 ) . Substitute x = 40 in the linear equation 5 x + 4 y = 200 . 5 ( 40 ) + 4 y = 200 200 + 4 y = 200 4 y = 200 − 200 y = 0 Thus, the value of y is 0 at x = 40 . Hence, the second coordinate is ( 40 , 0 ) . Therefore, the coordinates are ( 0 , 50 ) and ( 40 , 0 ) . Now determine whether the inequality is true or false using test point. Let the test point be ( 0 , 0 ) . Now substitute the test point ( 0 , 0 ) in 5 x + 4 y ≤ 200 . 5 ( 0 ) + 4 ( 0 ) ≤ 200 0 ≤ 200 It is noticed that the inequality 5 x + 4 y ≤ 200 is true. Thus, shade the half-plane that contain the test point ( 0 , 0 ) . That is, the half-plane below the line. Consider the equation (3). The given inequality in the equation is ≥ . Therefore, the solid line is used to join the coordinates of this equation. Then the equation (3) becomes, x = 10

Finite Mathematics and Calculus with Applications (10th Edition)

10th Edition

ISBN: 9780321979407

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 3.2, Problem 10E

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Finite Mathematics and Calculus with Applications (10th Edition)

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 linear programming problem by using graphical methods.

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Chapter 3 Solutions