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 Z = f(any) = x²y252²+ xy +7y² = 27де)g(x) = x² + xy + 7y² = 27 -2Using the method of Lagrange Multiplierof =Cliven functionConstantint 1²:12 Letaf atagag(as2+₁ 2+ )= a ( 23, 24)онду⇒ (2xy, x²) = 2 (2x+y, xc+.144)=>(any, a12²) = (a (20₁+y), A (2²+144))aДжу =вакand^ (2मty)2₁² = √(x + 144)Diving (3) by 42ny.272=(R+206) XX (81+149)2xy + 28y² = 22²³²+ my⇒ - 2x² + xy + 2ay ²= 0342120,(51(121701970·(2Scanned by TapScanner [15] (4) GIVEN: z =f(x, y) = x²y,where (x, y) is subject to the constraint:I: x² + xy + 7y²27, x > 0, y > 0.=a) Find MAX(z)andb) The point (x, y) = I so that MAX(z)AAB· C = ADⓇ(Find the maximum value of z, )Us the METHOD of the Lagrange Multiplier HINT:(providedf(x, y)4 =BA=A# 0,B #0C# 0,D#0'(Add on extra pagesas needed for yoursolution.ILLUSTRATION ofLagrange Solution

This is a quadratic equation in y , so find factorisation of equation (5) .

[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

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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

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
Scanned by TapScanner

[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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