\[\frac{\partial Q/\partial K}{\partial Q/\partial L} = \frac{L}{K} = \frac{r}{w} = \frac{1}{4} \Rightarrow L = \frac{K}{4}\]
\[Q = 4K^{1/2}L^{1/2} = 2K \Rightarrow K = \frac{Q}{2} L = \frac{Q}{8}\]
\[LTC(Q) = 2000K + 8000L = 1000Q\]
\[LAC(Q) = 1000\]
\[LMC(Q) = 1000\]