(a) Explanation Let x and y represents the number of units of the policy A and policy B respectively. The total amount of premium on theft or fire insurance and liability insurance is $50 and $40, respectively. That is, z = 50 x + 40 y . The policy A covers $10000 for fire or theft and $180,000 for liability and the policy B covers $15,000 for fire or theft and $120,000 for liability. Minimum theft or fire insurance required by the company is $300,000 minimum liability insurance is $3,000,000. From the above information, the linear programing problem can be stated as follows, Minimize z = 50 x + 40 y Subject to the constraints, 10 , 000 x + 15000 y ≥ 300 , 000 (1) 180 , 000 x + 120 , 000 y ≥ 3 , 000 , 000 (2) x ≥ 0 y ≥ 0 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 becomes, 10 , 000 x + 15000 y = 300 , 000 . Obtain any 2 coordinates of the above equation to plot on the line. Consider x = 0 , 30 and obtain the corresponding values of y respectively. Substitute x = 0 in the linear equation 10 , 000 x + 15000 y = 300 , 000 . 10 , 000 ( 0 ) + 15000 y = 300 , 000 15000 y = 300 , 000 y = 20 Thus, the value of y is 20 at x = 0 . Hence, the first coordinate is ( 0 , 20 ) . Substitute x = 30 in the linear equation 10 , 000 x + 15000 y = 300 , 000 . 10 , 000 ( 30 ) + 15000 y = 300 , 000 15000 y = 300 , 000 − 300 , 000 y = 0 Hence, the second coordinate is ( 30 , 0 ) . Therefore, the coordinates are ( 0 , 20 ) and ( 30 , 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 10 , 000 x + 15000 y ≥ 300 , 000 . 10 , 000 ( 0 ) + 15000 ( 0 ) ≥ 300 , 000 0 ≥ 300 , 000 It is noticed that the inequality 10 , 000 x + 15000 y ≥ 300 , 000 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 given inequality in the equation is ≥ . Therefore, the solid line is used to join the coordinates of this equation. Then the equation (2) becomes, 180 , 000 x + 120 , 000 y = 3 , 000 , 000 . Obtain any 2 coordinates of the above equation to plot on the line. Consider x = 0 , 50 3 and obtain the corresponding values of y respectively. Substitute x = 0 in the linear equation 180 , 000 x + 120 , 000 y = 3 , 000 , 000 . 180 , 000 ( 0 ) + 120 , 000 y = 3 , 000 , 000 120 , 000 y = 3 , 000 , 000 y = 25 Thus, the value of y is 25 at x = 0 (b) To determine To find: The number of units that to be purchased from each plan and the minimize the premium when the premium of the policy A is reduced to $25

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 11E

(a)

To determine

To find: The number of units that to be purchased on each plan and the minimum premium.

(b)

To determine

To find: The number of units that to be purchased from each plan and the minimize the premium when the premium of the policy A is reduced to $25

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Chapter 3.3, Problem 10E

Chapter 3.3, Problem 12E

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Chapter 3 Solutions

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 number of units that to be purchased on each plan and the minimum premium.

Solution Summary: The author explains that the minimum premium of 940 can be attained when 6 units of policy A and 16 units from policy B are purchased.