For each value of $\lambda$ the function $h(x,y) = x^2 + y^2 - \lambda(2 x + 6 y - 16)$ has a minimum value $m(\lambda)$.

(a) Find $m(\lambda)$
$m(\lambda) =$
(Use the letter L for $\lambda$ in your expression.)

(b) For which value of $\lambda$ is $m(\lambda)$ the largest, and what is that maximum value?
$\lambda =$
maximum $m(\lambda) =$

(c) Find the minimum value of $f(x,y)=x^2+y^2$ subject to the constraint $2 x + 6 y = 16$ using the method of Lagrange multipliers and evaluate $\lambda$.
minimum $f$ =
$\lambda =$

(How are these results related to your result in part (b)?)