4 A decision at the margin Hilary is a hardworking college s

4. A decision at the margin

Hilary is a hard-working college senior. One Saturday, she decides to work nonstop until she has answered 100 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.

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, isproblems.

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

Later, the teaching assistant in Hilary’s math course gives her some advice. “Based on past experience,” the teaching assistant says, “working on 35 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

3 hours working on problems, 1 hour reading

Time	Total Problems Answered
8:00 AM	0
9:00 AM	40
10:00 AM	70
11:00 AM	90
Noon	100

Solution

Time Total Problems answered Marginal Gains Marginal Gains /35 Marginal gains by reading books. 8:00 AM 0 9:00 AM 40 40 1.142857 1 10:00 AM 70 30 0.857143 1 11:00 AM 90 20 0.571429 1 Noon. 100 10 0.285714 1 1. The marginal gain from first hour of work = 40 2.The marginal gain from second hour of work = 30 3. She should spent 1 hour on problems and 3 hours reading.