Question: I was asked this on an aptitude test recently

> 
> Determine the next number in the sequence: $-2, 3, 27, 69, 129, \ ..$   
> 
>  A: $178$   
> 
>  B: $207$   
> 
>  C: $288$   
> 
>  D: $312$
> 
> 
> 

I've been racking my brain for a few days trying to find the solution but I can't figure it out.

Answer: 
computing the partial derivatives with respect to $K,L$
$$\frac{\partial F}{\partial K}=10\frac{1}{2}K^{-1/2}\sqrt{L}-r$$
$$\frac{\partial F}{\partial L}=10\sqrt{K}\frac{1}{2}L^{-1/2}-w$$
and solve the system
$$\frac{\partial F}{\partial K}=0$$
and $$\frac{\partial F}{\partial L}=0$$
Ok. I don't understand that. I can see that I forgot to include $p$. So I actually have:

$F(K,L)=10p\sqrt K\sqrt L -rK-wL $

If that makes any difference.