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 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.
(b) Write an equation for the line passing through the kinks of Nancy’s indifference curves. ________
(c) Write an equation for Nancy’s budget line. ___________
(d) Solve these two equations in two unknowns to determine the intersection of these lines. This happens at the point (x1, x2) = (40, 40).
(e) Given that she spends a total of 1,200 minutes studying, Nancy will maximize her overall score by spending ________ minutes studying for the first examination and ________ minutes studying for the second examination.