Explanation Given information: The function f ( x , y ) = 12 + 5 y − 20 x , and the polygon is shown in Figure 22(A) Concept Used: A linear function f ( x , y ) = a x + b y + c has no critical point, therefore the global maximum and minimum value of must occur on the boundary of a bounded domain Calculation: As f ( x , y ) = 12 + 5 y − 20 x is a linear function thus it has no critical point, therefore the global maximum and minimum value of must occur on the boundary of the polygon of Figure 22(A) As the polygon in figure 22(A) have boundary points ( − 3 , 0 ) , ( 1 , 0 ) , ( 0 , − 4 ) , ( 0 , 2 ) , checking value of function f ( x , y ) = 12 + 5 y − 20 x on boundary points f ( − 3 , 0 ) = 12 + 5 ( 0 )

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

4th Edition

ISBN: 9781319312886

Author: Rogawski, Jon, Adams, Colin, FRANZOSA, Robert

Publisher: W. H. Freeman

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Chapter 14.7, Problem 35E

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Find the global maximum and global minimum value of f(x,y)=12+5y−20x on the specified polygon shown in Figure 22(A) and indicate where they occur

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Chapter 14.7, Problem 34E

Chapter 14.7, Problem 36E

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Chapter 14 Solutions

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E

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Find the global maximum and global minimum value of f ( x , y ) = 12 + 5 y − 20 x on the specified polygon shown in Figure 22(A) and indicate where they occur

Solution Summary: The author explains that the global maximum and minimum value of f(x,y)=12+5y-20x must occur on the boundary of a bounded domain.

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Find the global maximum and global minimum value of f(x,y)=12+5y−20x on the specified polygon shown in Figure 22(A) and indicate where they occur

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Chapter 14 Solutions