Question

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 .

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+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.

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

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 values of the function
f(x,y,z)=x2y2z2 subject to the constraint x2+y2+z2=361.
Maximum value is:........... , occuring at ...............
points (positive integer or "infinitely many"). Minimum value is
........................ , occuring at ..................... points
(positive integer or "infinitely many").
Please fill in the blanks

Find the exact extreme values of the function z = f(x, y) = x^2
+ (y-19)^2 + 70 subject to the following constraints x^2 + y^2
<= 225 Complete the following: Fmin=____at(x,y) (__,__)
Fmax=____at(x,y) (__,__)

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...

2. Find the absolute maximum and minimum values of the function
f(x, y) = 2x^3 + y^4 on the unit disk.

Find the absolute maximum and minimum values of the function f
(x, y) = x^2 xy+on the region R bounded by the graphs of y = x^2
and y = x+ 2

Find the exact extreme values of the function z = f(x, y) =
(x-3)^2 + (y-3)^2 + 43
subject to the following constraints: 0 <= x <= 17
0 <= y <= 12
Complete the following: Fmin=____at(x,y) (__,__)
Fmax=____at(x,y) (__,__)

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