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2. A rectangle in the plane is placed in the first quadrant so that one corner O is at the origin and the two sides adjacent to O are on the axes. The corner P opposite to O is on the eurve r+ 2y = 1. Use Lagrange multipliers to find P so that the rectangle has maxirmum area.

2. A rectangle in the plane is placed in the first quadrant so that one corner O is at the origin and the two sides adjacent to O are on the axes. The corner P opposite to O is on the eurve r+ 2y = 1. Use Lagrange multipliers to find P so that the rectangle has maxirmum area.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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List of problems 1. Minimize the function f(z,y, 2) = y given the constraint g(z, y, 2) = z +y + = 1. 2. A rectangle in the plane is placed in the first quadrant so that one comer O is at the origin and the two sides adjacent to O are on the axes. The corner P opposite to O is on the curve r+ 2y = 1. Use Lagrange multipliers to find P so that the rectangle has maximum area. 3. Below we have plotted a curve G(z, v) = calong with VF. Find the candidates for the maximum and minimum values for F when restricted to G(2, y) -e. 4. The maximum value of f(r, y) subject to the constraint g(z, y) = 220 is 6900. The method of Lagrange multipliers gives A = 15. . Find an approximate value for the maximum of f(z, y) subject to the constraint g(z, y) = 217. %3D
Transcribed Image Text:List of problems 1. Minimize the function f(z,y, 2) = y given the constraint g(z, y, 2) = z +y + = 1. 2. A rectangle in the plane is placed in the first quadrant so that one comer O is at the origin and the two sides adjacent to O are on the axes. The corner P opposite to O is on the curve r+ 2y = 1. Use Lagrange multipliers to find P so that the rectangle has maximum area. 3. Below we have plotted a curve G(z, v) = calong with VF. Find the candidates for the maximum and minimum values for F when restricted to G(2, y) -e. 4. The maximum value of f(r, y) subject to the constraint g(z, y) = 220 is 6900. The method of Lagrange multipliers gives A = 15. . Find an approximate value for the maximum of f(z, y) subject to the constraint g(z, y) = 217. %3D
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