Question

Larry is a hard-working college freshman. One Saturday, he decides to work nonstop until he has answered 200 practice problems for his economics course. He starts work at 8:00 AM and uses a table to keep track of his progress throughout the day. He notices that as he gets tired, it takes him longer to solve each problem.Time Total Problems Answered8:00 AM 09:00 AM 8010:00 AM 14011:00 AM 180Noon 200Use the table to answer the following questions.The marginal, or additional, gain from Larry’s second hour of work, from 9:00 AM to 10:00 AM, isproblems.The marginal gain from Larry’s fourth hour of work, from 11:00 AM to noon, isproblems.Later, the teaching assistant in Larry’s economics course gives him some advice. "Based on past experience," the teaching assistant says, "working on 70 problems raises a student’s exam score by about the same amount as reading the textbook for 1 hour." For simplicity, assume students always cover the same number of pages during each hour they spend reading.Given this information, in order to use his 4 hours of study time to get the best exam score possible, how many hours should he have spent working on problems and how many should he have spent reading?0 hours working on problems, 4 hours reading1 hour working on problems, 3 hours reading2 hours working on problems, 2 hours reading3 hours working on problems, 1 hour reading

Answer 1

Answer:

• The marginal gain from Larry's second hour of work is 60 problems

• The marginal gain from Larry's fourth hour of work is 20 problems

• The best combination is 1 hour of working problems + 3 hours of reading

Explanation:

To get the marginal gain we subtract from the latest hour, in this case the second hour (140), the production from the previous hour (80). 140-80=60. It's always the same, the latest minus the previous one.

So let's do the same for the fourth hour:

Noon................200 problems

minus

11:00 AM..........180 problems

200-180= 20 problems

Now to know how many hours he should spend working on problems and reading, let's compare:

An hour of reading equals to 70 problems made; (because working on 70 problems raises a student’s exam score by about the same amount as reading the textbook for 1 hour).

hours of working problems         problems solved

0............................................................0

1.............................................................80

2............................................................140

3............................................................180

hours reading                    problems equivalent to hours read

4...............................................(4*70)=280

3...............................................(3*70)=210

2...............................................(2*70)=140

1................................................(1*70)=70

finally let's add up the two combinations (0 and 4, 1 and 3, 2 and 2, 3 and 1)

0 and 4_______________0+280= 280

1 and 3________________80+210=290

2 and 2_______________140+140=280

3 and 1________________180+70=250

And the best combination is 1 hour of working problems + 3 hours of reading=290