A firm uses labor and machines to produce output according to the production function f(L, M) = 4L^1/2 M^1/2 , where L is the number of units of labor used and M is the number of machines. The cost of labor is $40 per unit and the cost of using a machine is $10.
(a) If x-axis represents labor and y-axis represents machines, what is the slope of isocost line?
(b) Suppose that the firm wants to produce its output in the cheapest possible way. Find the number of machines it would use per worker.
(c) What is the cheapest way to produce an output of 40?
(d) How many units of labor and machines would the firm use to produce y units in the cheapest way? How much would this cost?