Consider the following production function for three firms operating in the same industry using capital (K) and labor (L) as inputs.

Firm A = Q=12K^0.5 L^0.25

Firm B =Q=10K^0.6 L^0.4

FirmC =O=K^3L

For each firm

Determine the firm's marginal product of capital function

Determine the firm's marginal product of labor function

Determine if the marginal product of capital function exhibits diminishing marginal returns

Determine if the marginal product of labor function exhibits diminishing marginal returns

Determine if the function exhibit increasing, constant or decreasing returns to scale.

Determine the function for the marginal rate of technical substitution

Determine if the production function has a diminishing marginal rate of technical substitution.

Derive the conditional input demand functions for labor and capital by Minimizing cost subject to output

Derive the conditional input demand functions for labor and capital by Maximizing output subject to cost constraint