University of Minnesota ECON 3101 - PS1 3. (POINTS: 50) (a) Solve the following problem, using the Lagrange method learned in lecture: (Points: 7.5) max - x - 12 r.y s.t. y= -x-4 (Eq1) Answer: (b) Solve the following problem, using the Lagrange method learned in lecture: (Points: 7.5) max - X-V x.y s.t. y= 17 (Eq2) Answer: C C C . 6 . OLGUniversity of Minnesota ECON 3101 - PS1 Now consider the following maximization problem, where (Eq ) and (Eq2) are set as inequal- ities max -x -x x.y s.t. ys -x-4 (ineqi) YST 17 (Ineq2) (c) Explain why you cannot use the Lagrange method as learned in lecture. (Points: 5) Answer: (d) Draw a graph and identify the feasible region (i.e., the region of points (x, y) such that they satisfy all constraints). Be sure to show the regions determined by each constraint. (Points: 15) Answer: OLG(e) Plot in your graph the solution found for items (a) and (b), and argue whether or not they could be solutions to the above problem. (Points: 10) Answer: (f) Write a similar problem to the one above, such that both have the same solution. (Points: 5) Hint: Use your answer in part (e) to understand how (Ineq ) and (Ineq2) are satisfied at the solution. Answer: OLG