Bob is a hardworking college senior One Thursday he decides

Bob is a hard-working college senior. One Thursday, he decides to work nonstop until he has answered 250 practice problems for his physics 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/ problems answered 8am- 0 9am- 100 10am- 175 11am- 225 noon- 250 The marginal, or additional, gain from Bob’s second hour of work, from 9:00 AM to 10:00 AM, is____ The marginal gain from Bob’s fourth hour of work, from 11:00 AM to noon, is______ problems. Later, the teaching assistant in Bob’s physics course gives him some advice. “Based on past experience,” the teaching assistant says, “working on 62.5 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 4 hours working on problems, 0 hours reading

Solution

The marginal gain from Bob\'s fourth hour of work, from 11:00 AM to noon is 25 problems.

62.5 problems = 1 hour of reading.

To get the best score possible, Bob should have read in those hours in which he solved less than 62.5 problems. He solved less than 62.5 problems from 10:00 AM to 11:00 Am and 11:00 AM to noon. He should have read in these two hours.

He should have spent 2 hours working on problems and 2 hours reading the textbook.