John takes microeconomics with Professor Nice. Professor Nice gives 2 exams, a mid-term and a final, and he marks each exam out of 100. Initially, the mid-term exam counts for 40% of the overall grade while the final exam counts for 60%. However, being nice, the professor introduces another option of weighing the midterm 20% and the final 80%, and each student's overall grade is calculated using the weighing option that gives him or her a higher overall grade. John strictly prefers a higher grade to a lower one. (a) Draw the indifference curve (for midterm and final exam marks) such that John's overall grade is 80. (b) Are John's preferences convex and (strongly) monotonic? Explain your