Maximize f ( x , y , z ) = x y + z 2...

Rapsinincke

Rapsinincke

Answered

2022-07-08

Maximize
f ( x , y , z ) = x y + z 2 ,
while 2 x y = 0 and x + z = 0. Lagrange doesnt seem to work.

Answer & Explanation

poquetahr

poquetahr

Expert

2022-07-09Added 18 answers

Since there are two constraints, we must use
f ( x , y , z ) = λ g + μ h .

We have
1. f ( x , y , z ) = x y + z 2
2. g ( x , y , z ) = 2 x y
3. h ( x , y , z ) = x + z
So we get
(1) f x = λ g x + μ h x y = 2 λ + μ (2) f y = λ g y + μ h y x = λ (3) f z = λ g z + μ h z 2 z = μ
with your constraint equations
(4) 2 x y = 0 (5) x + z = 0
Utilizing the system of equations (1) to (5), can you take it from here?

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