2. (15 points) You need to study for your math and physics finals. Your grade on both exams is proportional to the number of hours per day (so capped at 24 total hours) you spend studying that subject times your ability to absorb the material. You estimate that your ability to absorb math material falls from 100% by 4% for every hour you spend studying math and Page 2 of 4 by 3% for every hour you spend studying physics. Similarly, you find your ability to absorb physics material falls by 2% for each hour of studying math and by 5% for each hour of studying physics. (a) Find the optimal number of hours that you should study math and physics to maximize your average grade. Set the problem up and define all the variables and find the answer. (b) If you studied the optimal number of hours you found in part (a), which exam would you be better prepared for? (c) Now assume that your exam scores in both subjects improves by an additional 10% for every hour of the day that you do not study math or physics. Now what is the optimal number of hours spent studying for the two exams? (d) Examine the sensitivity of your answer to the additional 10\% benefit he gets from the time not studying. How would increasing the effect of this benefit affect your average grade? 2. (15 points) You need to study for your math and physics finals. Your grade on both exams is proportional to the number of hours per day (so capped at 24 total hours) you spend studying that subject times your ability to absorb the material. You estimate that your ability to absorb math material falls from 100% by 4% for every hour you spend studying math and Page 2 of 4 by 3% for every hour you spend studying physics. Similarly, you find your ability to absorb physics material falls by 2% for each hour of studying math and by 5% for each hour of studying physics. (a) Find the optimal number of hours that you should study math and physics to maximize your average grade. Set the problem up and define all the variables and find the answer. (b) If you studied the optimal number of hours you found in part (a), which exam would you be better prepared for? (c) Now assume that your exam scores in both subjects improves by an additional 10% for every hour of the day that you do not study math or physics. Now what is the optimal number of hours spent studying for the two exams? (d) Examine the sensitivity of your answer to the additional 10\% benefit he gets from the time not studying. How would increasing the effect of this benefit affect your average grade