# Consider the following production and cost functionsq=〖(10K^(2/5)+5L^(2/5))〗^(5/2)1250=20K+8LWhich implies〖MP〗_K=10〖(10K^(2/5)+5L^(2/5))〗^(3/2) K^(-3/5)〖MP〗_L=5〖(10K^(2/5)+5L^(2/5))〗^(3/2) L^(-3/5)What is the profit maximizing combination of K and L?

Question

Consider the following production and cost functions
q=〖(10K^(2/5)+5L^(2/5))〗^(5/2)
1250=20K+8L
Which implies
〖MP〗_K=10〖(10K^(2/5)+5L^(2/5))〗^(3/2) K^(-3/5)
〖MP〗_L=5〖(10K^(2/5)+5L^(2/5))〗^(3/2) L^(-3/5)
What is the profit maximizing combination of K and L?