5. A decision at the margin

Sean is a hard-working college senior. One Sunday, he decides to work nonstop until he has answered 50 practice problems for his physics 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 Answered

8:00 AM 0

9:00 AM 20

10:00 AM 35

11:00 AM 45

Noon 50

Use the table to answer the following questions.

The marginal, or additional, gain from Sean's first hour of work, from 8:00 AM to 9:00 AM, is___________________ problems.

The marginal gain from Sean's third hour of work, from 10:00 AM to 11:00 AM, is ____________________________ problems.

Later, the teaching assistant in Sean's physics course gives him some advice. "Based on past experience," the teaching assistant says, "working on 17.5 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?

Chose the right answer

0 hours working on problems, 4 hours reading

1 hour working on problems, 3 hours reading

3 hours working on problems, 1 hour reading

4 hours working on problems, 0 hours reading