2. Rachel needs to decide how to allocate her time. She needs to study for her upcoming exams in her economics course. There are 2 exams. Rachel's overall score in the economics course will be equal to the minimum of the two exams. Rachel has 1200 minutes to study for both exams. She wants to get the highest possible overall score in her class. If Rachel doesn't study for an exam, she'll get a zero on it. Every 10 minutes she spends studying for the first exam will increase her score by 1 point in that first exam. Every 20 minutes she spends studying for the second exam will increase her score by 1 point in that second exam. Studying for the first exam does not impact the score of the second exam and vice versa.

(a) On the graph below, draw a "budget line" that shows different combinations of scores on the two exams that she can get with 1200 minutes of studying. On the same graph draw two "indifference curves" for Rachel.

(b) Write equation for Rachel's "utility" function, and an equation for her "budget line".

(c) Solve Rachel's utility maximization problem. What is the overall score that Rachel can achieve?

(d) Given your answer in part (c), how much time should Rachel spend studying for each exam?