申論題

7.(13,5%) A manufacturer has $600,000 to spend on the production of a certain product and determines that if x units of capital and y unit of labor are allocated to production, than P units will be produced, where P is given by the Cobb-Douglas production function P(x, y) = 120x^0.8y^0.2. Suppose each unit of labor costs $3,000 and each unit of capital costs $5,000.

(i). How many units of labor and capital should be allocated in order to maximize production ?