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
Ely: 4x-274-0 => 4x = 2xy => AF ay
g = x2 + y2-2-0
tx2 24 2x => 242 = 2x2 => x2=42 X2+X2-2=0 Don't forget about the age old question of How do we know global politics exist?
2x2 -2 =>/x = 117 X=1 X2=42
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_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
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15.4 constramed optimization OT a Game Multipliers substitution Method Recall: H = fxx fyy-(fxy) If you want to learn more check out How do acids and bases affect how we function?
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
fx=-2x = 0 lo
co. ) Don't forget about the age old question of How did islam spread in the arabian peninsula?
fy = -52y = 0 ) cr @ (0,0)
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fx = -2x - fxy = 0
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
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)