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Use Lagrange multipliers to prove that the rectangle with maximum area that has a given perimeter p is a square. Let the sides of the rectangle be x and y and let f and g represent the area (A) and perimeter (p), respectively. Find the following. A = f(x, y) = xy p = g(x, y) = 2(x+y) V(x, y) =yi+xi Vg = yi +xi Then i = implies that x =y 2 Therefore, the rectangle with maximum area is a square with side length equal

Use Lagrange multipliers to prove that the rectangle with maximum area that has a given perimeter p is a square. Let the sides of the rectangle be x and y and let f and g represent the area (A) and perimeter (p), respectively. Find the following. A = f(x, y) = xy p = g(x, y) = 2(x+y) V(x, y) =yi+xi Vg = yi +xi Then i = implies that x =y 2 Therefore, the rectangle with maximum area is a square with side length equal

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.4: Linear Programming
Problem 7E
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Use Lagrange multipliers to prove that the rectangle with maximum area that has a given perimeter p is a square. Let the sides of the rectangle be x and y and let f and g represent the area (A) and perimeter (p), respectively. Find the following. A = f(x, y) = xy p = g(x, y) = 2 (x +y) V(x, y) =yi+xi Vg = yi +xi Then i = implies that x =y 2 Therefore, the rectangle with maximum area is a square with side length equai
Transcribed Image Text:Use Lagrange multipliers to prove that the rectangle with maximum area that has a given perimeter p is a square. Let the sides of the rectangle be x and y and let f and g represent the area (A) and perimeter (p), respectively. Find the following. A = f(x, y) = xy p = g(x, y) = 2 (x +y) V(x, y) =yi+xi Vg = yi +xi Then i = implies that x =y 2 Therefore, the rectangle with maximum area is a square with side length equai
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