Minimize the Function F(x) = X + Y, Subject to the Constraint

question 26

Short Answer

Minimize the function f(x) = x + y, subject to the constraint xy = 100, x > 0, y > 0. Use the method of Lagrange multipliers.
Enter your answer exactly as just (a, b), c where (a, b) gives the minimum and c is the Lagrange multiplier as a reduced fraction of form $\frac { d } { e }$ (no words or labels).

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Definitions:

Final Good

A product or service that is consumed by the end-user and does not require further processing or manufacturing.

Wood Pulp

The raw material used in the production of paper, made by chemically or mechanically processing wood fibers.

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Genuine Progress Indicator, an alternative to GDP that measures economic progress by also considering environmental degradation and social factors.

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The total market value of all final goods and services produced within a country's borders in a specified time period.