Consider a firm that has the production function F(K,L)= 3L^(1/2) K^(1/2). Suppose that the price of labor is $3 and the price of capital is $12.

a) What is the firms marginal rate of technical substitution?

b) If the firm is producing at the cost minimizing level, what is the optimal capital-labor ratio?

c) If the firm wants to produce units of their good at the cost minimizing level, how many units of capital and labor should it use? Show your work.

d) How much does it cost the firm to produce units of their good at the cost minimizing level? More generally, what is the firms cost function (in terms of )

Consider a firm that has the production function F(K,L)=3L21K21. Suppose that the price of labor is $3 and the price of capital is $12. a) What is the firm's marginal rate of technical substitution? If the firm is producing at the cost minimizing level, what is the optimal capital-labor ratio? If the firm wants to produce q units of their good at the cost minimizing level, how many units of capital and labor should it use? Show your work. How much does it cost the firm to produce q units of their good at the cost minimizing level? More generally, what is the firm's cost function (in terms of