1. (9 points) Suppose that the production process for a product requires 2 workers for every machine with a total factor productivity of 200. Thus, the production function can be represented as: Q=200*min{L,2K}where L is the number of workers and K is the number of machines use. The hourly wage (w) is $20 and the capital input price (r) is $28.
2. Calculate the level of L and K that allows this company to produce 4,000 units at the least possible cost. Make sure to show all your work.
3. Calculate the total cost corresponding to the input mix you found in part a). Make sure to show all your work.
4. Show this cost-minimizing input mix in the diagram below. Label this point "A". K on the vertical axis and L on the horizontal axis. Make sure to label the axes and each curve. Make sure to include the values of the vertical and horizontal intercepts corresponding to the isocost line. (Hint: In total you should have two curves: one isocost line and one isoquant.)