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ex3 Use La Grangian: Find max of f(x, y) = 4xy
subject to x2 + y2 =2
Wx2+422=0 2=fng
1  4xy  2 (x2 +422) = (4xy  xX2242 +22) O LX = 4y 2ax = 0 => 4y = 2^x=> 1 31 12
We also discuss several other topics like How do we know global politics exist?
Ely: 4x2740 => 4x = 2xy => AF ay
g = x2 + y220
tx2 24 2x => 242 = 2x2 => x2=42 X2+X22=0
2x2 2 =>/x = 117 X=1 X2=42

Roya yetu
x=1 x
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_ED=42411 Test CP (1, 1), (1,1), (1, 1), (1,1) f(x, y) = 4x4 f(1, 1) = f(1,1) = 4 4(1,1)=f(1, 1) = 4 Don't forget about the age old question of How to interact with the world, interact with peer and other adults?
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(1,1)
MAX=4
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Osubstitution
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15.4 constramed optimization OT a Game Multipliers substitution Method Recall: H = fxx fyy(fxy)
H70 &
min max HCO Saddle pt.
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ex1: use substitution method to find max off subject to
Z=> f(x, y, z)= 782Y 2 22 z=54
astu
f(x,y) = 78242  (54) 2 = 7X22642 If you want to learn more check out Who are the funk brothers? why were they central to the ‘motown sound’ and the success of the record label?
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fx=2x = 0 lo
co. )
fy = 52y = 0 ) cr @ (0,0)
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fxx2
fx = 2x  fxy = 0 We also discuss several other topics like How do acids and bases affect how we function?
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Study Soup Don't forget about the age old question of Who led the abbasid dynasty?
fy=52y  f4y = 52 H = fxx fyy (fxy) 2 H = (2) 152)  02 > 104 to max @coo)
z = 5y = 500)=0 f(x, y, z) = f(0,0,0)=Dr 7x2  y222 MAX=7 @ 10,0,0)
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☆ Laurange Multipliers
use L.G.M to find max of f subject to constraint g(x,y)=0 We also discuss several other topics like What is the focus of regulations administered by a government agency?
1 Construct The La Grangian Function
 ((x, y) = f(x, y)  & g(x, y) 2 solve the system a La Grange Multipliers
 2x=0
Lyo
Ly=0
g(x,y) = 0 ex 2: Use LaGrangian to find the max fəxy subject to Xt2y =76
l=frg
x+2y16=0  L=xy2(x+2y76) = xyax224 +767
2 x=y1=0 => a=yt
Italy = x27= 0 => X2x => X
9=x+2y76=0 studos y l
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38
X720)  76=0
2x76=0
x=38 => 4 = 3 = 19 Max of f(x, y) = xy is 38.19 = 722
@ (38, 19)
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