Suppose the production function of PowerGuns Co. is given by

Q = 25 LK 

where Q is the quantity of guns produced in the month, L is the number of workers employed, and K is the number of machines used in the production. The monthly wage rate is $3,000 per worker and the monthly rental rate for a machine is $6,000. Currently PowerGuns Co. employs 25 workers and 40 machines. Assume perfect divisibility of labor and machines. 

a. What is the current average product of labor for PowerGuns Co.? What is the current marginal product of machines? (Assume 1 unit increase in machines.) 

b. Does PowerGuns’ production function display increasing, decreasing, or constant returns to scale? Explain 

c. What is the total cost of the current production of PowerGuns in a month? What is the average cost to produce a shooting gun? Assuming the number of machines does not change, what is the marginal cost of producing one additional gun? 

d. What is the law of diminishing returns? Does this production display this characteristic? Explain .