You are taking two courses this semester, physics and economics. You have quizzes coming up in both classes. The following table shows your grade on each quiz for different numbers of hours spent studying for each quiz. (For the purposes of this problem, assume that each hour of study time can't be subdivided.) For instance, the table implies that if you spent 1 hour on economics and 2 hours on physics, you would get a 77 on the economics quiz and a 74 on the physics quiz. Hours of Study Economics Physics 0 70 60 1 68 2 3 85 78 77 82 74 1. Your goal is to maximize your average grade on the two quizzes. Use the idea of optimization to decide how much time you should spend studying for each quiz if you have only 1 hour in total to prepare for the two exams in other words, you will study 1 hour for one exam and 0 hours for the other exam). How would you allocate that single hour of study time across the two subjects? 2. Suppose that you have 2 hours instead of 1 hour to prepare quizzes, please apply marginal analysis to find the optimal solution by answering the following questions: (a) would you change the subject you would like to study in the first hour? (b) For the second hour, which subject would you choose to study? 3. Suppose that you have 3 hours instead of 2 hours to prepare quizzes, please apply marginal analysis to find the optimal solution by answering the following questions: (a) would you change the time allocation in the first two hours? (b) For the third hour, which subject would you choose to study