You are the manager of a new firm that can choose between two technologies for producing output using only labor. Technology A can produce two units of output for each hour of labor input. Technology B can produce three units of output for each hour of labor input up to 100 hours, and β units of output for each hour of labor above 100 hours. For what values of β is technology B more productive than technology A? [HINT: This is a challenge question! First, you should try to draw the graph of the production functions for technology A and B. Recall that technology B is more productive than technology A if the production function under technology B always lies above the production function under technology A. Now looking at your graph, figure out what is the minimum value of β for which the graph of technology B always lies above the graph of technology A.]