A decision at the margin

Hilary is a hard-working college senior. One Saturday, she decides to work nonstop until she has answered 250 practice problems for her physics course. She starts work at 8:00 AM and uses a table to keep track of her progress throughout the day. She notices that as she gets tired, it takes her longer to solve each problem.

Time	Total Problems Answered
8:00 AM	0
9:00 AM	100
10:00 AM	175
11:00 AM	225
Noon	250

Use the table to answer the following questions.

The marginal, or additional, gain from Hilary's first hour of work, from 8:00 AM to 9:00 AM, is

problems.

The marginal gain from Hilary's third hour of work, from 10:00 AM to 11:00 AM, is

problems.

Later, the teaching assistant in Hilary's physics course gives her some advice. "Based on past experience," the teaching assistant says, "working on 37.5 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 her 4 hours of study time to get the best exam score possible, how many hours should she have spent working on problems, and how many should she have spent reading?

0 hours working on problems, 4 hours reading

2 hours working on problems, 2 hours reading

3 hours working on problems, 1 hour reading

4 hours working on problems, 0 hours reading