3. The popularity of Mexican food has led to research into cilantro production (cilantro is an herb from the parsley family). You've discovered that cilantro responds well to an application of shredded economics textbooks, which provide an excellent source of nitrogen (many believe that economics textbooks are full of bull manure). You developed the following production function to represent the relationship between tons of shredded textbooks applied (x) and cilantro yield (y), in 100 pounds: y = 20x - 0.05x2 a. For each of the following price scenarios: (1) Estimate and plot TVP, AVP, and MVP; (2) Find the profit maximizing level of input required (how many tons of production economics textbooks should we purchase); and, (3) Show that, when the profit maximizing level of output is produced, MVP = MFC. Scenario 1: The input and output markets are competitive: P = 10, r = 15; Scenario 2: The output market is competitive, but your firm is a monopsony in the input market (the cost of production economics textbooks depends on how many you use): P = 20, r = 0.5x