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Find the maximum value of f(x,y) = 31-x² - y² on the line x + 5y = 26.

Find the maximum value of f(x,y) = 31-x² - y² on the line x + 5y = 26.

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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**Problem:** Find the maximum value of \( f(x, y) = 31 - x^2 - y^2 \) on the line \( x + 5y = 26 \). --- **Solution:** The maximum value of \( f(x, y) = 31 - x^2 - y^2 \) on the line \( x + 5y = 26 \) is \(\boxed{\text{insert answer}}\). (Simplify your answer.) --- *Note*: In order to solve this problem, the Lagrange multiplier method or substitution can be used by expressing one variable in terms of the other from the line equation, and then substituting into \( f(x, y) \).
Transcribed Image Text:**Problem:** Find the maximum value of \( f(x, y) = 31 - x^2 - y^2 \) on the line \( x + 5y = 26 \). --- **Solution:** The maximum value of \( f(x, y) = 31 - x^2 - y^2 \) on the line \( x + 5y = 26 \) is \(\boxed{\text{insert answer}}\). (Simplify your answer.) --- *Note*: In order to solve this problem, the Lagrange multiplier method or substitution can be used by expressing one variable in terms of the other from the line equation, and then substituting into \( f(x, y) \).
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