(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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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

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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.