(a)This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrangemultipliers to find the extreme values of the function subject to the given constraint.f(x, y, z) = x2 + y2 + z2, x2 + y2 + z2 + xy = 48maximum valueminimum value(b)Find the extreme values of f subject to both constraints. (If an answer does not exist, enter DNE.)f(x, y, z) = x + y + z;x²= 5, x + y = 4maximumminimum(c)Find the extreme values of f subject to both constraints. (If an answer does not exist, enter DNE.)f(x, y, z) = yz + xy;xy = 1, y2 + z2 = 81maximumminimum

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This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x, y, z) = x2 + y2+ z?, x² + y² + z² + xy = 48 maximum value minimum value

This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x, y, z) = x2 + y2+ z?, x² + y² + z² + xy = 48 maximum value minimum value

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.8: Linear Programming

Problem 36E

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Question

(a)
This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange
multipliers to find the extreme values of the function subject to the given constraint.
f(x, y, z) = x2 + y2 + z2, x2 + y2 + z2 + xy = 48
maximum value
minimum value
(b)
Find the extreme values of f subject to both constraints. (If an answer does not exist, enter DNE.)
f(x, y, z) = x + y + z;
x²
= 5, x + y = 4
maximum
minimum
(c)
Find the extreme values of f subject to both constraints. (If an answer does not exist, enter DNE.)
f(x, y, z) = yz + xy;
xy = 1, y2 + z2 = 81
maximum
minimum

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