Question

Minimize F=x^2+y^2 with x+4y=68

Answer 1

x+4y=68 is a constraint?

Answer 2

Correct, yes it is

Answer 3

G= Constraint equation
\[\nabla F=\lambda \nabla G\]

Answer 4

\[\nabla F={<2x,2y>}\]
\[\nabla G={<1,4>}\]

Answer 5

\[2x=\lambda*1\]
\[2y=\lambda*4\]

x+4y=68

Answer 6

what does lambda mean?

Answer 7

what does \[\lambda\] mean

Answer 8

Just a constant, you can use C instead of \[\lambda\]

Answer 9

Dude you are awesome, I appreciate it so much

Answer 10

From top two equation , we can see that y=4x

x+4y=68
x+16x=68
17x=68
x=4

Answer 11

plug that back in to find y

Answer 12

plug x=4 back into which equation?

Answer 13

x+4y=68
4y=64
y=16

@ btw , what Calculus are you taking?

Answer 14

Calc 2.... been absent so im playing catch up