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Use Lagrange multipliers to find the indicated extremum. Assume that x and y are positive. Minimize f(x, y) = V x2 + y2 Constraint: 10x + 20y – 10 = 0

Use Lagrange multipliers to find the indicated extremum. Assume that x and y are positive. Minimize f(x, y) = V x2 + y2 Constraint: 10x + 20y – 10 = 0

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CR: Review Problem Set
Problem 35CR: Maximize the function fx,y=7x+5y in the region determined by the constraints of Problem 34.
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Use Lagrange multipliers to find the indicated extremum. Assume that x and y are positive. Minimize f(x, y) Vx? + y? Constraint: 10x + 20y – 10 = 0 Step 1 First note that f(x, y) is minimum when g(x, y) = x- + y is minimum. Hence, we will minimize g(x, y) subject to the constraint h(x, y) —D 10х + 20y — 10. Define a new function F as F(x, у, а) %3D д(х, у) — ah(x, у) x2 + y? - 1(10x + 20y – 10). Find the partial derivatives of F with respect to x, y, and 1. F, (x, v. A) F,(x, v.a) = 2x Fy (x, y, a 2у — x, Y, a) = - 10 10х +
Transcribed Image Text:Use Lagrange multipliers to find the indicated extremum. Assume that x and y are positive. Minimize f(x, y) Vx? + y? Constraint: 10x + 20y – 10 = 0 Step 1 First note that f(x, y) is minimum when g(x, y) = x- + y is minimum. Hence, we will minimize g(x, y) subject to the constraint h(x, y) —D 10х + 20y — 10. Define a new function F as F(x, у, а) %3D д(х, у) — ah(x, у) x2 + y? - 1(10x + 20y – 10). Find the partial derivatives of F with respect to x, y, and 1. F, (x, v. A) F,(x, v.a) = 2x Fy (x, y, a 2у — x, Y, a) = - 10 10х +
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