3. A company manufactures a product which requires capital and labor to produce. The quantity, Q, of the product manufactured is given as a function Q = F(K, L) where K is the quantity of capital and...

Extracted text: 3. A company manufactures a product which requires capital and labor to produce. The quantity, Q, of the product manufactured is given as a function Q = F(K, L) where K is the quantity of capital and L is the quantity of labor used. One unit of capital costs $4 in ten thousands and one unit of labor costs $2 in thousands. The price of the product is fixed at $6 per unit. (a) Suppose the following Cobb-Douglas production function is used Q = F(K, L) 2K?/3 L²/3. How much capital and labor should the company use to maximize its profit? (b) Investigate the same problem as in (a) with Q = F(K, L) = 2K'/³ L²/3.