5. A decision at the margin

Crystal is a hard-working college sophomore. One Saturday, she decides to work nonstop until she has answered 250 practice problems for her math 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.

TimeTotal Problems Answered8:00 AM09:00 AM10010:00 AM17511:00 AM225Noon250Use the table to answer the following questions.

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

The marginal gain from Crystal's third hour of work, from 10:00 AM to 11:00 AM, isproblems.

Later, the teaching assistant in Crystal's math course gives her some advice. "Based on past experience," the teaching assistant says, "working on 87.5 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

1 hour working on problems, 3 hours reading

2 hours working on problems, 2 hours reading

4 hours working on problems, 0 hours reading