3. Remember Professor Goodheart from the first Problem Set. He gives two midterm exams and drops the worst of the two grades. With x being a student's grade on the first midterm and y her grade on the second midterm, compare (x,y)=(30,70) over (x,y)=(50,40). a) Which outcome does she prefer? b) Plot those indifference curves. Provide a function that describes the student's utility. C) As usual, each exam is worth 100 points. Assume that on the day of the midterms the student has another exam to study for - a 1 point increase on Professor Goodheart's first midterm exam costs 5 points on another exam (think of that as opportunity cost or time - what you forego/risk on the other exams), whilst there is little time conflict for the second midterm where a 1 point increase costs 2 points on the other exam. The student has a total (time) budget of 180 (think of the total score the student wants to get on two exams in the two classes). Identify the optimal bundle (grades) the student can achieve in your graph and as numbers. Explain. d) Is this a well-behaved problem? If yes, explain why. If no, describe all "non-normal" aspects