Question-3 (Cost Minimization) A firm uses labor and machines to produce output according to the production function f(L,M)=4L1/2M1/2 , 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.

- Draw an isocost line for this firm, showing combinations of machines and labor that cost $400 and another isocost line showing combinations that cost $200.

- Suppose that the firm wants to produce its output in the cheapest possible way. Find the number of machines it would use per worker. (Hint: The firm will produce at a point where the slope of the production isoquant equals the slope of the isocost line.)

- Sketch the production isoquant corresponding to an output of 40.

- Calculate the cost of producing 40 units at these factor prices: c(40; 10; 40).