Explanation Given: The maximum number of animals raised at a time is 16. The maximum number of goats raised at a time is 10. The cost to raise one goat is $25, and the cost to raise one pig is $75. The maximum cost available to raise the animals is $900. The profit gained from one pig is $40. The profit decreases from $40 to $35 for one pig raised. Explanation: The constraints as provided by the original problem are x + y ≤ 16 25 x + 75 y ≤ 900 x ≤ 10 x ≥ 0 y ≥ 0 The original objective function is z = 12 x + 40 y The graph of the linear inequalities as provided by the original solution is The optimal solution of the original problem is at the corner point ( 0 , 12 ) . Let the profit on one pig decrease from $40to $ ( 40 − c ) . The new objective function is z = 12 x + ( 40 − c ) y y = − 12 ( 40 − c ) x + z ( 40 − c ) The slope of the isoprofit lines for this objective function is − 12 ( 40 − c ) . The cost constraint inequality can be written as 25 x + 75 y ≤ 900 x + 3 y ≤ 36 The corresponding boundary line is x + 3 y = 36 y = − x 3 + 12 The slope of this boundary line is − 1 3

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, Problem 2EA

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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 new optimal solution for the number of goats and the number of pigs raised by Lisa if the profit decreases from $40 to $35 for one goat raised.

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The new optimal solution for the number of goats and the number of pigs raised by Lisa if the profit decreases from $40 to $35 for one goat raised.

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