Tully is taking a class with Professor Long. Professor Long has two tests a semester to determine a final grade - an easy midterm and a hard final.

The final grade is determined by the smaller of two numbers: half the score on the midterm, and the total score on the final.

Tully wants the highest final grade he can get. With the midterm grade on the "X" axis and the final exam grade on the "Y" axis draw two of Tully's indifference curves.

What is Tully's MRS? Are his preferences convex? strictly convex?