Rosa is a hard-working college sophomore. One Saturday, she decides to work nons
ID: 1145147 • Letter: R
Question
Rosa is a hard-working college sophomore. One Saturday, she decides to work nonstop until she has answered 250 practice problems for her physics 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 Rosa’s first hour of work, from 8:00 AM to 9:00 AM, isproblems.
The marginal gain from Rosa’s third hour of work, from 10:00 AM to 11:00 AM, isproblems.
Later, the teaching assistant in Rosa’s physics course gives her some advice. “Based on past experience,” the teaching assistant says, “working on 37.5 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 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
2 hours working on problems, 2 hours reading
3 hours working on problems, 1 hour reading
4 hours working on problems, 0 hours reading
Time Total Problems Answered 8:00 AM 0 9:00 AM 100 10:00 AM 175 11:00 AM 225 Noon 250Explanation / Answer
ANSWER:
Marginal gain from rosa first hour of work is 100 problems. ( total problem answered in 1st hour - total no of problems solved in 0th hour = 100 - 0 = 100)
Marginal gain from rosa third hour of work is 50 problems. ( total problem answered in 3e=rd hour - total problem answered by the end of 2nd hour = 225 - 175 = 50)
Rosa should make her decision at the margin as in each hour , she should select the option that will improve her grades to the maximum.
if she can solve more then 37.5 problems per hour, working on problems will raise her grades more that particular hout then reading.
The marginal gain for 1st hour is 100 problems. the marginal gain for 2nd hour is 75 problems. the marginal gain for the 3rd hour is 50 problems. she will stop after the 3rd hour because the marginal gain for 4th hour is 25 problems which is less then 37.5 problems per hour as her teacher suggested and so she will work 3 hours on solving problems and 1 hour reading.
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