Coca cola uses labour(L) and capital (k) in its production process. It estimates that the production function facing it is given by Q= K 0.5 L 0.5 . The company can sell a bottle of coke at GH4. The...

Coca cola uses labour(L) and capital (k) in its  production process.  It estimates that the production function facing it is given by Q= K^0.5
L^0.5. The company can sell a bottle of coke at GH4. The cost of a machine is GH3 and that of Man- hour is GH5. The firm's total cost if production at the end of production is expected to be GH 3000.

Required: Determine

1. The expression for the firm's marginal product of capital


2. The expression for the firm's marginal product of labour


3. The nature of the returns of the poduction


4. The optimal level of capital and labour usage


5. The firm’s firm’s profit at the optimal levels of capital and labour usage


6. The firm’s elasticity of output with respect to labour and capital and interpret it