An economy has a total of 320 units of labor and 80 units of capital to use on the production of 2 goods. The production functions for the goods are a function of the labor and capital used in each process. Specifically:

x= F(l,k) = (l*k)^.5

y= G(l,k) = 5(l*k)^.5

Explain why at any point on the PPF, each firm always has 4 times more labor than capital. If this is correct, then both the quantity of x and y can be written soley as a function of Kx. Find these functions, then use them to prove that the PPF function for this economy is y = 5x – 800.