Question

Find the maximum and minimum values of the function f(x,y,z)=x+2y subject to the constraints y^2+z^2=100 and x+y+z=5. I have: The maximum value is ____, occurring at (___, 5sqrt2, -5sqrt2). The minimum value is ____, occurring at (___, -5sqrt2, 5sqrt2). The x-value of both of these is NOT 1. The maximum and minimum are NOT 1+10sqrt2 and 1-10sqrt2, or my homework program is wrong.

Answer #1

Find the maximum and minimum values of the function
f(x,y,z)=3x−y−3 subject to the constraints x^2+2z^2=324 and
x+y−z=−6 . Maximum value is , occuring at ( , , ). Minimum value is
, occuring at ( , , ).

Find the maximum and minimum values of the function f(x, y, z) =
x^2 + y^2 + z^2 subject to the constraints x + y + z = 4 and z =
x^2 + y^2 .

The function f(x,y,z)= 4x+z^2 has an absolute maximum and
minimum values subject to the constraint of 2x^2+2y^2+3z^2=50. Use
Lagrange multipliers to find these values.

Find the maximum and minimum of the function f (x, y) = 6x − 2y
subject to the constraint . 3x^2 + y ^2 = 4

Find the extreme values of f subject to both constraints.
f(x, y, z) = x^2 + y^2 +z^2; x - y = 1, y^2 - z^2 = 1

Find the maximum and minimum values of the objective
function f(x, y) and for what values of
x and y they occur, subject to the given
constraints.
f(x, y) = 10x + 4y
x ≥ 0
y ≥ 0
2x + 10y ≤ 100
9x + y ≤ 54

Find the maximum and minimum values of f(x,y,z)=2x-2y-z on the
closed and bounded set 4x^2+2y^2+z^2 ≤ 1

Find the minimum of f(x,y,z) = x2 + y2 +
z2 subject to the two constraints x + 2y + z = 3 and x -
y = 4 by answering following questions
a) write out the lagrange equation involving lagrange
multipliers λ(lamba) and μ(mu)
b) solve for lamba in terms of x and y
c) solve for x,y,z using the constraints
d) determine the minimum value

Use the method of Lagrange multipliers to find the minimum value
of the function
f(x,y,z)=x2+y2+z2
subject to the constraints x+y=10 and 2y−z=3.

Find the minimum and maximum values of the function
f(x,y)=x2+y2f(x,y)=x2+y2 subject to the given constraint
x4+y4=2x4+y4=2.
(The minimum is not not zero, DNE, or NONE, I have tried all of
those)

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