The Cobb-Douglas production function is given by z=P(x,y)=Ax^alpha y^(1-alpha), where x is the amount of labor in work-hours and y is the amount of capital, A is a constant, and 0

1. Write the formula for the production function z=P(x,y).
2. What is the production when8 work-hours and27 units of capital are provided?
3. Determine the relationship between the amounts of labor and capital required for the production of 200 units.
4. If16 work-hours are available, find the amount of capital needed in the production of 100 units.