Question

Hubert is a hard-working college junior. One Sunday, he decides to work nonstop until he has answered 150 practice problems for his economics 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 | 60 |

10:00 AM | 105 |

11:00 AM | 135 |

Noon | 150 |

Use the table to answer the following questions.

The marginal, or additional, gain from Hubert’s second hour of work, from 9:00 AM to 10:00 AM, isproblems.

The marginal gain from Hubert’s fourth hour of work, from 11:00 AM to noon, isproblems.

Later, the teaching assistant in Hubert’s economics course gives him some advice. “Based on past experience,” the teaching assistant says, “working on 52.5 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 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

Answer #1

The marginal, or additional, gain from Hubert’s second hour of
work, from 9:00 AM to 10:00 AM, is **45**
problems.

(Marginal gain = 105 - 60 = 45)

The marginal gain from Hubert’s fourth hour of work, from 11:00
AM to noon, is **15**
problems.

(Marginal gain = 150 - 135 = 15)

1 hour working on problems, 3 hours reading

(Marginal gain from first hour = 60 - 0 = 60 which is greater than
marginal gain from reading. However, marginal gain from second hour
= 45 problems which is less than marginal gain from reading. Thus,
only 1 hour will be spent working on problems and 3 hours are thus
spent on reading.)

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