Professor Goodheart always gives two midterms in his communications class. He only uses the higher of the two scores a student gets on the midterms when he calculates the course grade. (Adapted from Varian Workouts)(a)You want to maximize your course grade. Let x1be your score on the midterm 1 and x2beyour score on midterm 2. Which combination do you prefer, x1 = 20 and x2= 70 or x1 = 60and x2= 60?(b) Draw a graph showing an indifference curve of the all the combination of scores that you like exactly as much as x1 = 20 and x2= 70. Also draw an indifference curve showing all the combinations you like as much as x1= 60 and x2= 60.(c)Do you have convex preferences over these combinations?

(d) You are also taking a course with Professor Stern who also gives two midterms. Instead of discarding the lower grade, he discards the higher one. Let x1be the score on the first midterm, and x2be the score on the second midterm. Which combination do you prefer, x1= 20 and x2= 70 or x1= 60 and x2= 50?(e)Draw a graph showing an indifference curve of the all the combination of scores that you like exactly as much as x1= 20 and x2= 70. Also draw an indifference curve showing all the combinations you like as much as x1= 60 and x2= 50.