Assignment #1 (7/26, due on 7129, Friday) The following study schedule is recommended: (a) Complete each reading assignment by the deadline, you will be prepared for the class; (b) Take notes carefully during lecture and review them at least once every two days. Discuss your notes and homework within your study group. Do not hesitate to come to me to clarify whatever points you find ambiguous; (c) Try to do your homework the same or next day after class, what you learned are still fresh. Put your major efforts into understanding your notebook and solving the problem sets. 1.] (10 mks). Each year a farmer has 100 acres of land, 3880 machine hours and 2500 labor hours to grow grain and vegetables. Each acre of grain requires 15 labor hours and 40 machine hours per year, while each acre of vegetables needs 35 labor hours and 25 machine hours per year. The prot per acre of grain is $ 50, and that per acre of vegetables is $68. Formulate the farmer's decision problem by following the WWW procedure discussed in class. In other words, you need to identify the choice variables (what you can do), the objective function (what you want), and the constraints (what you can NOT do). Note: This is a Linear Programming (LP) problem because all functions are linear. If any of the obtained objective or constraint functions are non-linear, it will be called non-linear programming; if any of the involved choice variables are integers, it will be called integer programming. 1.2 (10 mks each). In parts a) and b) below, assume px = $1, py = $5, I = income = $21. Solve the U-max problem for each of the following two utility mctions: (a) U = xyz, x, y 2 0; (b) U = x'Bym, x, y 2 0; (c) now, let p; = p, Py = $5, I = $21, nd the u-max solution for U = xyz, x, y 2 0; (d) let px = 1, p3,. = p, I = $21, nd the unmax solution for U = xyz, x, y 2 0; (e) show that the u-max solution for U = xyz, given (p1, y, I), is x =.f(px. .0 I) = 170px): andy = 309x, Pr: 1): 211(3)). Hint: Use equal MU/$ method. Note that part a) is \"identical\" to the example solved in class. 1.3 (10 mks each). Solve Problems 2.2, 2.4 and 2.6 on Page 32. 1.4 (10 mks). Update one of the following four tables in EckertWest (2005) by your student number with this rule: update Table 1.1 if the last digit of your student number is between 0 and 2, table 1.2 if the last digit of your student number is between 3 and 5, table 1.3 if between 6 and 7, and table 1.10 if between 8 and 9. It will be sufcient if you provide one or two new columns. Suppose your # is, for example, xxxxxxxl , then you should nd the data in Table 1.1 for one or two recent years, and provide a short paragraph summarizing the change from the last column in the table to your new column. If new data is not available (show evidence such as one or two screen shots), update the next table. For example, if you are supposed to update Table 1.2 but no new data can be found (need to provide evidence), then you update Table 1.3; if you are supposed to update Table 1.10 and no new data can be found, then you update Table