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Step 1 Recall that if f(x, y) has a maximum or minimum subject to the constraint g(x, y) = 0, then it will occur at of the critical numbers of the function F defined as follows where. d is a Lagrange multiplier. F(x, y, 1) = f(x, y) – 1g(x, y) We wish to find the maximum of f(x, y) = xy subject to the constraint x + 5y – 10 = 0. So, we let g(x, y) = x + 5y – 10 and we define the new function F as follows. %3D (^ 'x)6 F(x, y, 1) = f(x, y) – 1g(x, y) | al x+ 5y - 10 Ax = x+ 5y - 10

Step 1 Recall that if f(x, y) has a maximum or minimum subject to the constraint g(x, y) = 0, then it will occur at of the critical numbers of the function F defined as follows where. d is a Lagrange multiplier. F(x, y, 1) = f(x, y) – 1g(x, y) We wish to find the maximum of f(x, y) = xy subject to the constraint x + 5y – 10 = 0. So, we let g(x, y) = x + 5y – 10 and we define the new function F as follows. %3D (^ 'x)6 F(x, y, 1) = f(x, y) – 1g(x, y) | al x+ 5y - 10 Ax = x+ 5y - 10

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 17EQ
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Step 1 Recall that if f(x, y) has a maximum or minimum subject to the constraint g(x, y) = 0, then it will occur at of the critical numbers of the function F defined as follows where. d is a Lagrange multiplier. F(x, y, 1) = f(x, y) – 1g(x, y) We wish to find the maximum of f(x, y) = xy subject to the constraint x + 5y – 10 = 0. So, we let g(x, y) = x + 5y – 10 and we define the new function F as follows. %3D (^ 'x)6 F(x, y, 1) = f(x, y) – 1g(x, y) | al x+ 5y - 10 Ax = x+ 5y - 10
Transcribed Image Text:Step 1 Recall that if f(x, y) has a maximum or minimum subject to the constraint g(x, y) = 0, then it will occur at of the critical numbers of the function F defined as follows where. d is a Lagrange multiplier. F(x, y, 1) = f(x, y) – 1g(x, y) We wish to find the maximum of f(x, y) = xy subject to the constraint x + 5y – 10 = 0. So, we let g(x, y) = x + 5y – 10 and we define the new function F as follows. %3D (^ 'x)6 F(x, y, 1) = f(x, y) – 1g(x, y) | al x+ 5y - 10 Ax = x+ 5y - 10
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