You run a plant that produces machines with the help of a number of working teams that work

by assembly line. The technology is reflected in the following product function:

q = 5KL

where q is the number of machines produced per. week, K is the number of assembly lines and L is the number

work team. Rental prices pr. assembly line, r, is $ 50,000 per week and each work team costs,

w, $ 25,000 pr. week. The production costs are given by the labor and capital costs plus

$ 10,000 in raw material costs per. machine. The system has 5 assembly lines that can not be changed

short term.

a) What is the cost function for your plant - ie how much will it cost to produce

q machines? Find the marginal cost and average cost function. How

does the average cost vary with production?

b) How many work teams are required to produce 250 machines? What is then

the average cost per machine?

c) You will be asked to make recommendations on the design of a new factory.

What capital / labor rate should the new plant have if one is to minimize

the cost of any level of production?