Q: If f(L,K)=L.5K.5, w=1, and v=25, what is the cheapest cost of producing 30 units of out put?
A: First, we need two equations to find the optimal input bundle.
Use RTS=w/v, which is K/L=1/25 or 25K=L.
Also, use L.5K.5 =30.
Combing these two we have 30=(25K).5K.5 or30=5K.
Therefore, K=6 and hence L=25(6)=150.
Hence the minimum cost of making q=30 units of output is 1(150)+25(6)=150+150=300.