Question

Nancy Lerner is trying to decide how to allocate her time in studying for her economics course. There are two examinations in this course. Her overall score for the course will be the minimum of her scores on the two examinations. She has decided to devote a total of 1,200 minutes to studying for these two exams, and she wants to get as high an overall score as possible. She knows that on the first examination if she doesn’t study at all, she will get a score of zero on it. For every 10 minutes that she spends studying for the first examination, she will increase her score by one point. If she doesn’t study at all for the second examination she will get a zero on it. For every 20 minutes she spends studying for the second examination, she will increase her score by one point.a) On the graph below, draw a "budget line" showing the various combinations of scores on the two exams that she can achieve with a total of 1,200 minutes of studying. On the same graph, draw two or three "indifference curves" for Nancy. On your graph, draw a straight line that goes through the kinks in Nancy’s indifference curves. Label the point where this line hits Nancy’s budget with the letter A. Draw Nancy’s indifference curve through this point.(c) Write an equation for Nancy’s budget line. (e) Given that she spends a total of 1,200 minutes studying, Nancy will maximize her overall score by spending how many minutes studying for the first examination and how many minutes studying for the second examination?

Answer 1

Answer:

x=400, y=800

Explanation:

In order to maximize the minimum score of the two exams.

overall score = min [exam 1, exam 2]

score exam 1= 0.1x; where x is the number of minutes spent

studying on exam 1

score exam 2= 0.5y; where y is the number of minutes spentstudying on exam 2

We find the  first derivative shows that the marginal benefit of time spent on exam 1 is two times that of exam two, she will then  spend twice as much time studying for exam 2 as for exam 1 to  secure  same score on both.

The budget equation : 1200 = x + y

x=time spent for exam 1

y=time spent for exam 2

substitute y into the above equation

1200= x + 2x

1200= 3x

x=400

y=2x

y=400*2

y=800

So she should spend 400 minutes studying for exam one and 800minutes studying for exam 2.

which gives score 40 in both score and exam.