Math for Econ II, Written Assignment 4 (28 points)Due Friday, October 3Please write neat solutions for the problems below. Show all your work. If you only write the answer with no work,you will not be given any credit.•Write your name and recitation section number.•Staple your homework if you have multiple pages!1. (4 pts) The figures below show the optimal point (marked with a dot) in three optimization problems with thesame constraint. Arrange the corresponding values ofλfrom smallest to largest. Assumeλ >0 in each case.Briefly justify your answer.(In diagram (I), the bottom is not labeled “fx= 1.” It is the curvef= 1, with thex-axis labeled below it)(I)(II)(III)
2. (4 pts) Find the global maximum and global minimum values (if they exist) ofx2+y2in the regionx+y≤1.If there is no global max, justify why. If there is no global minimum, justify why.