Explanation Let x represents the number of engines to ship plant I and y represents the number of engines to ship to plant II. Plant I needs at least 45 engine, it can be represented as x ≥ 45 . Plant II needs at least 32 engines, it can be represented as y ≥ 32 . Two assembly plants at most 120 engines. it can be represented as x + y ≤ 120 . Plant I gives Miers $20 in rebates its products for each engine and plant II give similar $15 rebates, it can be represented as 20 x + 15 y ≥ 1500 . Produced of plant I and plant II cannot be negative, it can be represented as x ≥ 0 and y ≥ 0 . Thus, the system of inequalities are x ≥ 45 , y ≥ 32 , x + y ≤ 120 , 20 x + 15 y ≥ 1500 , x ≥ 0 and y ≥ 0 . Engines to ship to plant I costs is $30 and Engines to ship to plant II costs is $40 it can be represented as x ≥ 0 and y ≥ 0 , minimize z = 30 x + 40 y . x ≥ 45 (1) y ≥ 32 (2) x + y ≤ 120 (3) 20 x + 15 y ≥ 1500 (4) Consider the equation (1). Since the given inequality in the equation is ≥ , the solid line is used to join the coordinates of this equation. Now, replace the symbol ≥ by the symbol = in given equation (1). Then, the equation (1) becomes, x = 45 . The equation x ≥ 45 represents the set of all points whose x coordinates are greater than 45. That is, all points to the right of the solid vertical line x = 45 . Use the test point to determine the half plane which is to be shaded. Let the test point be ( 0 , 0 ) . Substitute the test point ( 0 , 0 ) in x ≥ 45 , 0 ≥ 45 It is noticed that the inequality is false for the test point. Thus, shade the half-plane that does not contain the test point ( 0 , 0 ) . Consider the equation (2). Since the given inequality in the equation is ≥ , the solid line is used to join the coordinates of this equation. Now, replace the symbol ≥ by the symbol = in given equation (2). Then the equation (2) becomes, y = 32 . The equation y ≥ 32 represents the set of all points whose x coordinates are greater than 32. That is, all points to the right of the solid vertical line y = 32 . Use the test point to determine the half plane which is to be shaded. Let the test point be ( 0 , 0 ) . Substitute the test point ( 0 , 0 ) in y ≥ 32 , 0 ≥ 32 It is noticed that, the inequality is false for the test point. Thus, shade the half-plane that does not contain the test point ( 0 , 0 ) . Consider the equation (3). 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 (3) with an “equals” sign. Then, the equation becomes, x + y = 120 . Obtain any 2 coordinates of the above equation to plot on the line. Consider x = 0 , 120 and obtain the corresponding values of y respectively. Substitute x = 0 in the linear equation x + y = 120 . 0 + y = 120 y = 120 Thus, the value of y is 120 at x = 0 . Hence, the first coordinate is ( 0 , 120 ) . Substitute x = 120 in the linear equation x + y = 120 . 120 + y = 120 y = 120 − 120 y = 0 Hence, the second coordinate is ( 120 , 0 ) . Therefore, the coordinates are ( 0 , 120 ) and ( 120 , 0 ) . Use the test point to determine the half plane which is to be shaded. Let the test point be ( 0 , 0 ) . Now substitute the test point ( 0 , 0 ) in x + y ≤ 120 . 0 + 0 ≤ 120 0 ≤ 120 It is noticed that the inequality x + y ≤ 120 is true. Thus, shade the half-plane that contain the test point ( 0 , 0 )

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 3.3, Problem 7E

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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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