Question

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.

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

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

Answer 1

Time	Total problems Answered	Marginal or additional gain
8:00 AM	0	-----
9:00AM	40	(40 - 0) = 40
10: 00AM	70	(70 - 40) = 30
11:00 AM	90	(90 - 70) = 20
Noon	100	(100 -90) =10

The marginal, or additional gain from Hilary first hour of work from 8:00 AM to 9:00 AM is 40 problems.

The marginal gain from Hilary third hour of work from 10:00 AM to 11:00 AM is 20 problems.

Based on past experience,” the teaching assistant says, “working on 35 problems raises a student’s score by about the same amount as reading the textbook for 1 hour.”

Hilary will solved the problems until he is able to solve 35 problems or more. If he is able to solve less than 35 problems per hour, then he will devote each successive hour to reading textbook.

The above table depcits that till 9AM, Hilary is able to solve more than 35 problems.

Hence, Hilary will devote 1 hours working on problems and 3 hours on reading.

Answer: Option (B)