A firm uses labor and machines to produce output according to the production function f(L,M)=4L raise to 1/2 M raise to1/2 where L is the number of units labor used and M is the number of machines. The cost of labor is Php. 40 per unit and the cost pf using machine is Php. 10.
a. Draw an isocost line for this firm, showing combinations of machines and labor that cost Php. 400 and another isocost line showing combinations that cost Php. 200. What is the slope of these 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. Sketch the production isoquant corresponding to an output 40. Calculate the amount of labor and the number of machines that are used to produce 40 units of output in the cheapest possible way, given the above factor prices.