As head of the planning commission of Eastern Motors, your job is to determine where to locate a new plant. The only inputs used in your cars are steel and labor and the production function is Cobb-Douglas where $$f(S,L) = S^{0.5} L^{0.5}$$ where $S$ is tons of steel and $L$ is units of labor.
You can locate your plant either in country A or country B. In country A, steel costs 7\$ and labor costs 7\$. In country B, steel costs \$8 and labor costs 6\$. In which country should the company locate its new plant so as to minimize costs per unit of output, minimize the cost of production?
F(L,S) = L^.5 S^.5 MRTS= MP (S)/ MP(L)=Price of steel/price of labour
COUNTRY A
L/S=1
L=S
TCost =7L+7S
Country B l/s=8/6 L=4S/3
T cost = 8S+6L
i dont know what to do next?