[15] (4) GIVEN: z = f(x, y) = x²y, where (x, y) is subject to the constraint: T: x² + xy + 7y² 27, x > 0, y > 0. a) Find MAX(z) and = (Find the maximum value of z, ) b) The point (x, y) = I so that MAX(z) = f(x, y) Α = λB - A - B Us the METHOD of the Lagrange Multiplier HINT: (provided = AD A + 0,B+0 C# 0,D#0' Add on extra pages as needed for your solution.
[15] (4) GIVEN: z = f(x, y) = x²y, where (x, y) is subject to the constraint: T: x² + xy + 7y² 27, x > 0, y > 0. a) Find MAX(z) and = (Find the maximum value of z, ) b) The point (x, y) = I so that MAX(z) = f(x, y) Α = λB - A - B Us the METHOD of the Lagrange Multiplier HINT: (provided = AD A + 0,B+0 C# 0,D#0' Add on extra pages as needed for your solution.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
please calculate the first image attached just like the second image attached please
in the seocnd image i tried to calcuate but got confused, can you please help and finish the calculations please
![[15] (4) GIVEN: z =
f(x, y) = x²y,
where (x, y) is subject to the constraint:
I: x² + xy + 7y²
27, x > 0, y > 0.
=
a) Find MAX(z)
and
b) The point (x, y) = I so that MAX(z)
A
AB
· C = ADⓇ
(Find the maximum value of z, )
Us the METHOD of the Lagrange Multiplier HINT:
(provided
f(x, y)
4 =B
A
=
A# 0,B #0
C# 0,D#0'
(Add on extra pages
as needed for your
solution.
ILLUSTRATION of
Lagrange Solution](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F767da4a8-c644-4919-9393-25d8fa6c982f%2Fe7ced278-66f3-4f2f-841b-1cdfc5e51770%2Fw0wg9qo_processed.png&w=3840&q=75)
Transcribed Image Text:[15] (4) GIVEN: z =
f(x, y) = x²y,
where (x, y) is subject to the constraint:
I: x² + xy + 7y²
27, x > 0, y > 0.
=
a) Find MAX(z)
and
b) The point (x, y) = I so that MAX(z)
A
AB
· C = ADⓇ
(Find the maximum value of z, )
Us the METHOD of the Lagrange Multiplier HINT:
(provided
f(x, y)
4 =B
A
=
A# 0,B #0
C# 0,D#0'
(Add on extra pages
as needed for your
solution.
ILLUSTRATION of
Lagrange Solution
![[15] (4) GIVEN: z = f(x, y)
=
x²y,
where (x, y) is subject to the constraint:
T: x² + xy + 7y² = 27, x > 0, y > 0.
a) Find MAX(z)
and
(Find the maximum value of z,)
b) The point (x, y) er so that MAX(z) = f(x, y)
=
AB
=
ADA= B
A# 0,B #0
C# 0,D#0'
Us the METHOD of the Lagrange Multiplier HINT:
SA
lc
(provided
f(x,y) = x²y
g(x, y) = x² + xy + 7y²
L.S. { xf = nvg
g=27
of=2&g (2xy, x²)=2(2x + y₂ x +14y)
{ 2x+y = 2xy^²¹
2хул
2 x + 14y=x²²x²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F767da4a8-c644-4919-9393-25d8fa6c982f%2Fe7ced278-66f3-4f2f-841b-1cdfc5e51770%2Fwxef80m_processed.png&w=3840&q=75)
Transcribed Image Text:[15] (4) GIVEN: z = f(x, y)
=
x²y,
where (x, y) is subject to the constraint:
T: x² + xy + 7y² = 27, x > 0, y > 0.
a) Find MAX(z)
and
(Find the maximum value of z,)
b) The point (x, y) er so that MAX(z) = f(x, y)
=
AB
=
ADA= B
A# 0,B #0
C# 0,D#0'
Us the METHOD of the Lagrange Multiplier HINT:
SA
lc
(provided
f(x,y) = x²y
g(x, y) = x² + xy + 7y²
L.S. { xf = nvg
g=27
of=2&g (2xy, x²)=2(2x + y₂ x +14y)
{ 2x+y = 2xy^²¹
2хул
2 x + 14y=x²²x²
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