Question

Using langragrean, Find the values of x, y and z that minimise (x^4 + y^4 + z^4 )^1/4 subject to the constraint x + 8y + 27z = 10.

Answer #1

Find the values of x, y and z that minimise (x 4 + y 4 + z 4 )
1/4 subject to the constraint x + 8y + 27z = 10?

b)
Minimize
Subject to:
Z = 5x – 2y
x + y ≤ 50
3x + 8y ≥ 90
y ≥ 10
x ≤
32
x, y ≥ 0
Total cost
First constraint
Second constraint
Third constraint
Fourth constraint
Non-negativity constraint

Use Lagrange Multipliers to find the extreme values of f(x, y,
z) = x + 2y^2 - z^2
subject to the constraint x^2 + 4y^2 + 2z^2 = 17.

Solve the following problems by USING Lagrange multipliers.
(a) Find the maximum and minimum values of f(x, y, z) = x^2 +
y^2 + z^2 subject to the constraint (x − 1)^2 + (y − 2)^2 + (z −
3)^2 = 4
(b) Find the maximum and minimum values of f(x, y, z) = x^2 +
y^2 + z^2 subject to the constraints (x − 1)^2 + (y − 2)^2 + (z −
3)^2 = 9 and x − 2z...

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 .

Use Lagrange multipliers to find the extremal values of
f(x,y,z)=2x+2y+z subject to the
constraint
x2+y2+z2=9.

Use the method of Lagrange multipliers to find the maximum and
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G(x,y,z) = x2+y2+z2 = 25. Note the
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Use Lagrange multipliers to find the minimum value of f ( x , y
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z = 49. The minimum value of f ( x , y ) subject to 2 x − 3 y − 4 z
= 49 is

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

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.

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