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Homework answers / question archive / You have 8 hours to study for two final exams
You have 8 hours to study for two final exams. The exam for course A is worth 25% of your grade, and the exam for course B is worth 50% of your grade. The first hour you spend on studying for either exam will increase your score on it by 10 percentage points, the second hour will increase your grade on it by an additional 9 percentage points, the third hour will increase your grade on it by an additional 8 percentage points, and so forth. How will you allocate your time? Explain your answer in terms of marginal analysis.
To design a solution to this question, think in terms of the marginal increase in the overall class grade that each additional study hour will provide for each exam. Intuitively, we know that exam B contributes twice as much to the overall class grade (50%) as exam A, so studying for exam B should account for the first hour of study time (and likely the first several hours).
The strategy thus becomes a question of starting with studying for exam B, and continuing to study additional hours for exam B until the contribution to the overall class grade is less than the contribution of spending the first hour on exam A.
We can construct a simple table to illustrate the marginal benefit of each hour of study for each exam. The cell values in the table give the incremental increase in the overall class grade for each incremental hour of study.
| Exam (Weight) | Hour 1 | Hour 2 | Hour 3 | Hour 4 | Hour 5 | Hour 6 | Hour 7 | Hour 8 |
|---|---|---|---|---|---|---|---|---|
| 10% | 9% | 8% | 7% | 6% | 5% | 4% | 3% | |
| A (25%) | 2.50 | 2.25 | 2.00 | 1.75 | 1.50 | 1.25 | 1.00 | 0.75 |
| B (50%) | 5.00 | 4.50 | 4.00 | 3.50 | 3.00 | 2.50 | 2.00 | 1.50 |
We can see from the table that the sixth hour of study for exam B gives an incremental 2.5 points toward the overall class grade, which is equivalent to the first hour of study for exam A (a 10% increase weighted at 25% = 2.5 points).
If our study time was limited to 6 hours, we would indifferent between the choice of the sixth hour devoted to exam B, or the first hour of studying for exam A. Each is worth additional 2.5 points.
But with 8 hours, we would choose both of these options, and then devote our final (8th) hour of study to the next best option: the second hour of study for exam A, which is worth 2.25 points.
Another way of allocating the time is simply constructing a table that ranks each exam-hour option in terms of points:
| Option | Value |
|---|---|
| B - 1 | 5.00 |
| B - 2 | 4.50 |
| B - 3 | 4.00 |
| B - 4 | 3.50 |
| B - 5 | 3.00 |
| B - 6 or A - 1 | 2.50 |
| A - 2 | 2.25 |
| B - 7 or A - 3 | 2.00 |
| A - 4 | 1.75 |
| A - 5 or B - 8 | 1.50 |
| A - 6 | 1.25 |
| A - 7 | 1.00 |
| A - 8 | 0.75 |
Working down this list, we see that our 8th hour of study should be allocated to exam A for a second hour.
