Find the optimal demand functions for capital and labour for this firm I'm trying to solve this question which states:

Suppose that a profit maximizing producer has a production function described by Q = K^3/4 L^1/4 and faces the general isocost line (TC = rK + wL). 

Find the optimal demand functions for capital and labor for this firm.

Here's what I've done and know:

I've solved for the MP1(labor) and MP2(capital):
MP1 = 1/4 (K^3/4 * L^-3/4 )
MP2 = 3/4 (K^-1/4 * L^1/4 )

I also know that MP1 / MP2 = w / r. 

Can someone point out a suggestion to solve for K and L, the optimal demand functions?

Thanks
A firm requieres capital $K\in\mathbb{R}_+$ and labor $L\in\mathbb{R}_+$ to produce the final good $Q$. The technology is of Cobb-Douglas type $Q:(K,L)\mapsto K^{\alpha}L^{1-\alpha}$, here $\alpha=0.75$. Denote the capital rent by $r$ and the worker's wage by $w$. Production costs are then given by $C:(K,L)\mapsto rK+wL$. Instead of maximizing profits, the firm wants to minimize costs to produce a given quantity $\bar{Q}&gt;0$ (look up the duality of $\min-\max$ problems in producer theory). We end up with the following programm
\begin{align}
\min_{K,L}~C(K,L)\quad\text{s.t.}~~Q(K,L)\geq\bar{Q}.
\end{align}
Which is 
\begin{align}
\min_{K,L}~(rK+wL)\quad\text{s.t.}~~K^{.75}L^{.25}\geq\bar{Q}.
\end{align}
Set up the lagragian
\begin{align}
\mathcal{L}=rK+wL+\lambda(\bar{Q}-K^{.75}L^{.25}).
\end{align}
Note that the constraint is binding (Why? Look that up too!) The FOCs are given by 
\begin{align}
\frac{\partial \mathcal{L}}{\partial K}=0\\
\frac{\partial \mathcal{L}}{\partial L}=0\\
\frac{\partial \mathcal{L}}{\partial\lambda}=0
\end{align}
Solve for $K$ and $L$.