(a) Explanation Given: Premium of policy A = $50 Premium of policy B = $40 Minimum limit of fire/theft insurance = $300,000 Minimum limit of liability insurance = $3,000,000 Policy A Policy B Fire/theft (in $) 10,000 15,000 Liability (in $) 180,000 120,000 Premium (in $) 50 40 Explanation: Let x be the number of units of policy A purchased and y be the number of units of policy B purchased. The given information can be summarized in the table as follows: Type of policy Policy A Policy B Total Number of units purchased x y Fire/theft (in $) 10,000 15,000 ≥ 300,000 Liability (in $) 180,000 120,000 ≥ 3,000,000 Premium (in $) 50 40 Use the table to write the constraints as follows: 10 , 000 x + 15 , 000 y ≥ 300 , 000 180 , 000 x + 120 , 000 y ≥ 3 , 000 , 000 Divide both sides of the first constraint by 5000 and both sides of the second constraint by 60,000, and then rewrite the constraints as follows: 2 x + 3 y ≥ 60 3 x + 2 y ≥ 50 The number of units of policy A and policy B cannot be negative: x ≥ 0 and y ≥ 0 The objective function to be minimized gives the total premium (b) To determine The number of units of policy A and policy B that should be purchased to minimize the premium. Also, the cost of minimum premium.

Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)

11th Edition

ISBN: 9780133886818

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

Publisher: PEARSON

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Chapter 3.3, Problem 11E

(a)

To determine

The number of units of policy A and policy B that should be purchased to minimize the premium. Also, the cost of minimum premium.

(b)

To determine

The number of units of policy A and policy B that should be purchased to minimize the premium. Also, the cost of minimum premium.

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Chapter 3.3, Problem 10E

Chapter 3.3, Problem 12E

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Chapter 3 Solutions

Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)

Ch. 3.1 - Graph each linear inequality. x + y 2 Ch. 3.1 - Graph each linear inequality. y x + 1 Ch. 3.1 - Graph each linear inequality. x 2 y Ch. 3.1 - Graph each linear inequality. y x 3 Ch. 3.1 - Graph each linear inequality. 4x y 6 Ch. 3.1 - Graph each linear inequality. 4y + x 6 Ch. 3.1 - Graph each linear inequality. 7. 4x + y 8 Ch. 3.1 - Graph each linear inequality. 2x y 2 Ch. 3.1 - Graph each linear inequality. x + 3y 2 Ch. 3.1 - Graph each linear inequality. 2x + 3y 6

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The number of units of policy A and policy B that should be purchased to minimize the premium. Also, the cost of minimum premium.

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The number of units of policy A and policy B that should be purchased to minimize the premium. Also, the cost of minimum premium.

The number of units of policy A and policy B that should be purchased to minimize the premium. Also, the cost of minimum premium.

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Chapter 3 Solutions