Help me with Linear programming and Lagrangian method pretty please?

I don't like linear programming so..

I take it Calvin has £100 to spend on milk and cookies.

I'm interpreting your u as $u=c^{0.6}m^{0.4}$. Is that correct?

Using the price of milk and the price of cookies can you write the constraint function?

The u is the utility yeah so its $u=c^{0.6}m^{0.4}$. The constraint should be 6c+2m=100. Income of £100 and price of cookie is £6 and milk is £2

OK, so we can write

$g(c,m)=6c+2m \\ u(c,m)=c^{0.6}m^{0.4}$.

Now you need to solve

$u_c=\lambda g_c \\ u_m=\lambda g_m \\ 3c+m=50$

Still don't understand. Have a skip through this. http://www.youtube.com/watch?v=HLTyVlVQD8U

Is this woman doing it right? been following her technique.

Actually having taken a better look at that video I think the following is easier:
$\displaystyle 10 x^{-0.5} y ^{0.5} + 40 \lambda =0$

$\displaystyle 10 x^{0.5} y ^{-0.5} + 120 \lambda =0$

$\displaystyle 40x + 120 y =300000$

Write them in terms of x/y and divide through by 10.

$\displaystyle \left( \frac{x}{y}\right) ^{-0.5} =- 4 \lambda$

$\displaystyle \left( \frac{x}{y}\right) ^{0.5} =- 12 \lambda$

Divide the second equation by the first.

$\frac{x}{y}=3$ so $\displaystyle x=3y$

Use the constraint to get 24y=30000 so y=1250 and x=3750 and the maximum value for N is about 43300.

Man I'm such a thicko.