Dimex Fabrication Co., a small manufacturer of sheet-metal body parts for a major U.S. automaker, estimates its long-run production function to be
Q = −0.015625K3L3 + 10K2L2
where Q is the number of body parts produced daily, K is the number of sheet-metal presses in its manufacturing plant, and L is the number of labor-hours per day of sheet-metal workers employed by Dimex. Dimex is currently operating with eight sheet-metal presses.
a. What is the total product function for Dimex? The average product function? The marginal product function?
b. Managers at Dimex can expect the marginal product of additional workers to fall beyond what level of labor employment?
c. Dimex plans to employ 50 workers. Calculate total product, average product, and marginal product.