1.You are the owner of a motorbike company that currently has two different factories, an old one and a new one. The old factory uses an old technology that requires large amounts of labor to produce motorbikes. The production technology for the old firm is given by Fo(L) = 7*L^1/2 . The new factory uses a much more modern production technology given by Fn(L) = 8*L^1/2 .

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

b.Suppose that you want to produce 1000 motorbikes. How many motorbikes 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 motorbikes (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?

d.It turns out that you can upgrade your old factory to make it just as efficient as the new factory. To pay for the upgrade, you can take out a loan that will be paid back in equal annual installments for the rest of the lifetime of your business. If you plan on producing 1000 motorbikes every year, what is the largest annual payment you are willing to make to upgrade your old factory?