Question

Am i doing this lagrange multiplier problem wrong?

Answer 1

Function: f(x,y)=.20x^2+5y+.30y^2+15y

Answer 2

Constraint: x+y=2000

Answer 3

lol lagrange?

Answer 4

Method of Lagrange:\[\nabla f = \lambda \nabla g\]

Answer 5

which translates to: \[(f _{x},f_{y})=\lambda(g _{x},g_{y})\]

Answer 6

g is the constraint

Answer 7

Doing those partials yields:
\[(.4x,20+.6y)=\lambda(1,1)\]

Answer 8

so we have the following equalities:\[.4x=\lambda\] and \[20+.6y=\lambda\]

Answer 9

Since they both = labda we can say:
\[.4x=20+.6y

Answer 10

which can be written as:
\[.4x-.6y=20\]

Answer 11

Found my error :)

Answer 12

Thanks for being a great spectator :P

Answer 13

lol