Alice is choosing how to allocate her time between studying for exams and exercising. Assume she values one hour of studying as much as one hour of exercising and as a constant marginal rate of substitution. She has 12 hours a day she can allocate between both.

a) Write an equation representing Alice's constraint.

b) Write an equation representing Alice's preferences

c) How much time does Alice allocate to studying? Explain the rationale for your answer.