Question

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) (__,__)

Answer #1

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) (__,__)

Determine the global extreme values of the function
f(x,y)=2x3+2x2y+2y2,x,y≥0,x+y≤1
fmin=
fmax=

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 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 .

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 ( , , ).

Use Lagrange Multipliers to find the extreme values of f(x,y,z)
= x2 + 3y subject to the constraints x2 +
z2 = 9 and 3y2 + 4z2 = 48.

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.

f(x,y)=xy ; 4x^2+y^2=8
Use Lagrange multipliers to find the extreme values of the
function subject to the given constraint.

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

Use the method of Lagrange multipliers to find the extreme
values of f(x,y)=
x^(2) + y^(2) − xy − 4 subject to the constraint x + y = 6.

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