Julia’s grade in her history class depends on a term paper and a final exam. Her grade will be the minimum of the two scores. She has 1,200 minutes to devote to her history class, and she wants to maximize her grade. For the term paper, if she doesn’t work on it at all, she will get a zero. For every ten minutes she spends writing, her score will go up by 1 point. If she doesn’t study for the final exam, she will also get a zero. For every 20 minutes spent studying, she will increase her score by one point.
a. Putting the final exam score on the y-axis and the term paper score on the x-axis, graph Julia’s budget constraint. This is all the combinations of scores on the two assignments that are possible given 1200 minutes of study time. On the same graph, draw a few of Julia’s indifference curves.
b. Draw a straight line that goes through the all the kinks in Julia’s indifference curves. What is the equation of this line? (Let y=score on final exam and x = score on term paper)
c. What is the equation for Julia’s budget constraint?
d. Solve these two equations for the two unknowns. What is the optimal combination of scores that Julia should achieve? e. How many minutes will Julia spend writing her term paper and how many minutes will she spend studying for the final exam?