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.

Q1) The marginal, or additional, gain from Sean's first hour of work, from 8:00 AM to 9:00 AM, is problems.

Q2) 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,

Q3) 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 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