9. Production of a certain item is given by the Cobb-Douglas production z = P(x, y) = ray, where r is the amount of labor in work-hours and y is the amount of capital. (a) What is the production when 81 hours and 16 units of capital are provided? (b) Determine the relationship between the amounts of labor and the capital re- quired for the production of 20 units. (c) Sketch the level curve at a production of 20 units in the ry-plane. (d) If 40 work-hours are available, find the amount of capital needed in the produc- tion of 20 units