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Use Lagrange multipliers to find the indicated extremum. Assume that x and y are positive. Maximize f(x, y) = xy Constraint: x + 5y – 10 = 0

Use Lagrange multipliers to find the indicated extremum. Assume that x and y are positive. Maximize f(x, y) = xy Constraint: x + 5y – 10 = 0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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Use Lagrange multipliers to find the indicated extremum. Assume that x and y are positive. Мaximize f(x, у) %3D ху Constraint: x + 5y – 10 = 0 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 one of the critical numbers of the function F defined as follows where a is a Lagrange multiplier. F(x, у, 1) %3D f(x, у) — 1g(x, у) 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. F(x, у, 1) f(x, У) — 1g(x, у) = xy – 1
Transcribed Image Text:Use Lagrange multipliers to find the indicated extremum. Assume that x and y are positive. Мaximize f(x, у) %3D ху Constraint: x + 5y – 10 = 0 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 one of the critical numbers of the function F defined as follows where a is a Lagrange multiplier. F(x, у, 1) %3D f(x, у) — 1g(x, у) 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. F(x, у, 1) f(x, У) — 1g(x, у) = xy – 1
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