Find the maximum value of f(x1,x2,. ,xn) = (x1.x₂ -In)¹/" where ₁,..., In are positive numbers and 1 + x₂ + ... + n = c where c is a positive constant.

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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Find the maximum value of f(x₁,2,,n) = (x₁ - T₂ · ... · Tn)²¹/" where x₁,..., n
are positive numbers and 2₁ +22+...+ n = c where c is a positive constant.
Use Lagrange Multipliers to find the volume of the largest open-top box that has
120 m² of surface area, and 70 m of edge length (sum of all edges).
Recall that for two constraint functions g₁, 92, the method of Lagrange multipliers
states that Vf=>₁Vg₁ + X₂Vg2.
Transcribed Image Text:Find the maximum value of f(x₁,2,,n) = (x₁ - T₂ · ... · Tn)²¹/" where x₁,..., n are positive numbers and 2₁ +22+...+ n = c where c is a positive constant. Use Lagrange Multipliers to find the volume of the largest open-top box that has 120 m² of surface area, and 70 m of edge length (sum of all edges). Recall that for two constraint functions g₁, 92, the method of Lagrange multipliers states that Vf=>₁Vg₁ + X₂Vg2.
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