Using Multiple Factories You are the owner of a car company that currently has two different factories, an old one and a new one. The old factory is uses an old technology that requires large amounts of labor to produce cars. The production technology for the old firm is given by fold(L) = 5L^1/2 . The new factory uses a much more modern production technology given by fnew(L) = 10L^ 1/2 .

(a) What are costs as a function of output for each individual factory?

(b) Suppose that you want to produce 1000 cars. How many cars will you produce at the old factory and how many will you produce at the new factory?

(c) Derive an expression for the total cost of producing y cars (assuming that you always divide production between the factories in the optimal way). How does this cost function compare to the individual factory cost functions?