Suppose you manage a plant that produces engines by teams of workers using assembly machines. The technology is summarized by the production function Q = 4KL where Q is the number of engines produced per week, K is the number of assembling machines, and L the number of labor teams. Each assembly machine rents for r = $12,000 per week and each labor team costs w = $3,000 per week. Total engine costs are given by the cost of labor teams and assembling machines plus $2,000 per engine for raw (component) materials. Your plant currently has a fixed installation of 10 assembly machines as a part of its design.

a. What is the total cost function [TC = f(Q)] for your plant- namely, how much will it cost to produce Q engines given the production function and input costs above? What are the average [ATC = f(Q)] and marginal costs [MC = f(Q)] of producing Q engines? How do average costs vary with output?

b. How many labor teams are required for producing a batch of 80 engines given the plant's current makeup? What is the average total cost per engine?