Sam is a hard-working college junior. One Saturday, he decides to work nonstop u

Question

Sam is a hard-working college junior. One Saturday, 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 8:00 AM 9:00 AM 10:00 AM 11:00 AM Total Problems Answered 60 105 135 150 Use the table to answer the following questions. The marginal, or additional, gain from Sam's first hour of work, from 8:00 AM to 9:00 AM, is problems The marginal gain from Sam's third hour of work, from 10:00 AM to 11:00 AM, is problems. Later, the teaching assistant in Sam's economics course gives him some advice. "Based on past experience," the teaching assistant says, "working on 22.5 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 2 hours working on problems, 2 hours reading 3 hours working on problems, 1 hour reading

Explanation / Answer

The marginal, or additional gain from Sam's first hour of work, from 8:00 AM to 9:00 AM is = ( 60 - 0) = 60 problems

The marginal gain from Sam's third hour of work, from 10:00 AM to 11:00 AM, is = (135 - 105) = 30 problems.

Sam will try to maximize his score from his 4 hours of study. If solving 22.5 problems raises a student's score by about the same amount as reading the textbook for 1 hour, Sam will spend his hours working on problems until his additional gain from next hour of work is less than 22.5 problems. That next hour sam will use to read the textbook in order to maximize his exam score.

Here, The marginal gain from Sam's third hour of work, from 10:00 AM to 11:00 AM, is = (135 - 105) = 30 problems which is greater than 22.5 problems. So, Sam will definitely use 3 hours working on problems. But his marginal gain from the fourth hour of work, from 11:00 AM to Noon, is = ( 150 - 135) = 15 problems which is less than 22.5 problems. So, Sam will use his this hour of work on reading textbooks.

Answer - Option 4

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