1. ## Langrange Multiplier Method

Need help using the Lagrange Multiplier Method on this problem. I could easily optimize this with direct substitution but I need to know how to solve it using this method.

$z=f(x,y)=3(x-5)^2+4y+1307$

The Function is constrained by $x+y=144$

so I have $L(x,y)=3(x-5)^2+4y+1307-lambda(x+y-144)$

Then $Lx(x,y)=6(x-5)-lambda=0$
$Ly(x,y)=4-lambda=0$
$g(x,y)=x+y-144=0$

2. Originally Posted by Brokensound723

$z=f(x,y)=3(x-5)^2+4y+1307$

The Function is constrained by $x+y=144$

so I have $L(x,y)=3(x-5)^2+4y+1307-lambda(x+y-144)$
I get

$L(x,y,\lambda)=3(x-5)^2+4y+1307+\lambda (x+y-144)$

with

$L_x=6(x-5)+\lambda =0$

$L_y=4+\lambda =0$

$L_{\lambda}=x+y-144=0$

Now solve the system

$6(x-5)+\lambda =0$ ...(1)

$4+\lambda =0$ ...(2)

$x+y-144=0$ ...(3)