Question

What is 5, 6, and 7? I think 1-4 is correct.  

Suppose a student has 9 hours available to study Economics, Spanish and Psychology with an estimate of performance based on hours of study for upcoming exams. Hours Economics Spanish Psychology 30 to-amooooo 1. If our student spent all their time studying Economics, what will her grades be in Economics, Spanish and Psychology (i.e. her total # of points)? Economics: 91 Spanish: 30 Psychology: 35 2. If our student spent all her time studying Spanish, what would her grades be (i.e. her total # of points)? Economics: 20 Spanish: 99 Psychology: 35 3. If our student spent all her time studying Psychology, what would her grades be (i.e. her total # of points)? Economics: 20 Spanish: 30 Psychology: 99 4. If our student divided her time evenly among all 3 subjects, what would her grades be (i.e. her total # of points)? Economics: 71 Spanish: 77 Psychology: 79 5. How would you recommend that our student allocate her study hours, if her goal is to maximize her total # of points? 6. Graph the gain in scores for studying the first second, third...ninth hour of studying a) Economics, b) Spanish, c) Psychology on three separate graphs. How would you describe the graphs you drew? What can you say about the gains of studying more and more hours of, e.g., Economics? 7. What can you say about the cost of studying fewer and fewer hours of, e.g. Economics if her goal is to maximize her total # of points?

Answer 1

Yep 1-4 are correct.

5. To determine the point where the study should allocate her study hours for maximum total # of points, we draw a table that shows the marginal points gained per hour of studying in each subject and add to that subject where it is higher first.

Hours	Marginal points gained in economics	Marginal points gained per hour in spanish	Marginal points gained per hour in psychology
0
1	39-20=19	21	18
2	56-39=17	14	16
3	71-56=15 (And so on)	12	10
4	11	9	8
5	4	5	5
6	2	4	3
7	1	2	2
8	1	1	1
9	1	1	1

Now The student will allocate each hour to where the marginal points gained is highest.

So starting from 1st hour- spanish (21 points gained)

2nd hour- Economics (19 points gained)

3rd hour- Psychology (18 points gained)

4th hour - Economics (17 points gained)

5th hour- Psychology (16 points gained)

6th hour- Economics (15 points gained)

7th hour- spanish (14 points gained)

8th hour- spanish (12 points gained)

9th hour- economics (11 points gained)

So the student will allocate 4 hours to economics, 3 hours to spanish and 2 hours to psychology for gaining a maximum total # of points= 82+79+69=228

6. You can graph the table in the question with Number of hours on X-axis and the score of economics on Y-axis (And then for spanish) to get upward sloping graphs (But the slope will be decreasing)

From the graphs we can say that all of them are upward sloping graphs showing diminishing returns. The Economics one has high returns uptil the 4th hour and then the returns start diminishing very highly. So gains of studying more and more hours of economics are very low with marginal gains dropping very steeply

The graph for spanish has high returns uptil the 4th hour too and then starts diminishing (But the returns are less for the first 4 hours and the diminishing is not as strong as that of economics, so the returns in latter hours are higher).

The graph for psychology also has high returns initially and achieves diminishing returns around 3rd or 4th hour and diminishes similarly to spanish one(Less diminishing compared to that of Economics with higher gains in the additional hours). Gains of studying psychology and spanish are comparatively higher for further hours of studying.

7. The cost of studying fewer and fewer hours of economics is very high as the initial marginal gains for studying economics is very high compared to spanish and psychology, therefore it will reduce the total # of points significantly. Cost of reducing hours of studying spanish and psychology is also high but not as high as that of economics.

Hope it helps Do ask for any clarifications required.