Consider the production function Q = 20K 1/2 L 1/2. The firm operates in the short run with 100 units of capital.a. The firm’s short-run production function is Q = __________.c. The average product of labor function is AP = __________.d. The marginal product of labor function is MP = _________. Show that the marginal diminishes for all levels of labor usage.e. Assuming that the firm in question 2 is in the long run where its fixed endowment is $1000, wage rate is $10, and interest payment for capital is $5, what is the combination of capital-labor ratio that will maximize output? Show the graphical combination. Assume that the wage rate falls to $5, what is the new combination on the same graph?f. What kind of returns to scale is depicted for each of the Cobb-Douglas production functions below? Explain. Q = K 1/4 L 1/4; Q = K 1/2 L 2/3