I've been stuck on a profit maximization problem. The question is as follows: Find the optimal ratio of capital per worker for the following profit function:$$\pi (K,L) = 10Y(K,L) -wL-rK $$ where $w = 4,r=8 $ and $Y(K,L)= 2L^{1/5}K^{4/5}$. Also, K stands for capital and L for labor.
I've taken the partials with respect to both K and L and found that there's no critical point. How else could I maximize this function?