ex3 Use La Grangian: Find max of f(x, y) = 4xy
subject to x2 + y2 =2
1 - 4xy - 2 (x2 +42-2) = (4xy - xX2-242 +22) O LX = 4y -2ax = 0 => 4y = 2^x=> 1 31- 12
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Ely: 4x-274-0 => 4x = 2xy => AF ay
g = x2 + y2-2-0
tx2 24 2x => 242 = 2x2 => x2=42 X2+X2-2=0
2x2 -2 =>/x = 117 X=1 X2=42
_ED=424-11 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?
15.4 constramed optimization OT a Game Multipliers substitution Method Recall: H = fxx fyy-(fxy)
min max HCO Saddle pt.
ex1: use substitution method to find max off subject to
Z=> f(x, y, z)= 7-82-Y 2 -22 z=54
f(x,y) = 7-82-42 - (54) 2 = 7-X2-2642 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?
fx=-2x = 0 lo
fy = -52y = 0 ) cr @ (0,0)
fx = -2x - fxy = 0 We also discuss several other topics like How do acids and bases affect how we function?
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) 1-52) - 02 > 104 to max @coo)
z = 5y = 500)=0 f(x, y, z) = f(0,0,0)=Dr 7-x2 - y2-22 MAX=7 @ 10,0,0)
☆ 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
g(x,y) = 0 ex 2: Use LaGrangian to find the max fəxy subject to Xt2y =76
x+2y-16=0 | L=xy-2(x+2y-76) = xy-ax-224 +767
2 x=y-1=0 => a=yt
Italy = x-27= 0 => X-2x => X-
9=x+2y-76=0 studos y l
X720) - 76=0
x=38 => 4 = 3 = 19 Max of f(x, y) = xy is 38.19 = 722
@ (38, 19)