[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) [A AB Us the METHOD of the Lagrange Multiplier HINT: { c = 2B-4-B A= C (provided = 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) [A AB Us the METHOD of the Lagrange Multiplier HINT: { c = 2B-4-B A= C (provided = A# 0,B=0 C# 0,D 0' (Add on extra pages as needed for your solution. ILLUSTRATION of Lagrange Solution
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please calcutate the first image attached
please do not im saying do not calculate as the second image attched please calculate first image attached differently
Transcribed Image Text:Z = f(any) = x²y
2
52²+ xy +7y² = 27
де)
g(x) = x² + xy + 7y² = 27 -
2
Using the method of Lagrange Multiplier
of =
Cliven function
Constantint 1²:
12 Let
af at
ag
ag
(as
2+₁ 2+ )= a ( 23, 24)
он
ду
⇒ (2xy, x²) = 2 (2x+y, xc+.144)
=>
(any, a
12²) = (a (20₁+y), A (2²+144))
a
Джу =
вак
and
^ (2मty)
2₁² = √(x + 144)
Diving (3) by 4
2ny.
272
=
(R+206) X
X (81+149)
2xy + 28y² = 22²³²+ my
⇒ - 2x² + xy + 2ay ²= 0
3
4
2120,
(5
1
(1
21701970
·(2
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![[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%2F69006781-6ec7-4986-97af-ec5a6fbf065e%2F99011494-37c3-4985-856a-34222dcd06a4%2Few2kit_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
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