Question

3) Lori is studying economics and political science. She can read 30 pages of political science per hour but only 5 pages of economics per hour. This week she has a 50-page assignment in economics and a 150-page assignment in political science. Because of her job, she cannot devote more than 10 hours to studying these subjects this week. She realizes she cannot complete all of her assignments but is determined to complete at least 30 pages of her economics reading. Draw a graph with pages of economics on the horizontal axis and pages of political science on the vertical axis. On this graph, show the possibilities that are consistent with the constraints that Lori has imposed on herself. (She is allowed to read ahead in either subject.) Label key points on your graph with their numerical values.

Answer 1

Sol:
The objective is to draw a graph with possibilities that are consistent with the constraints that Felicity has
imposed on herself. The possibilities that consistent with the constraints are the elements of the budget
set. She has a time budget that is limited to 10 hours. A budget constraint is in the form of the familiar
equation p1x1 + p2x2 = m. For this problem, let’s use psxs + pexe = t, where ps is the time-cost (hours per
page) for political science reading, where pe is the time-cost (hours per page) for economics reading, xs is
the number of pages of political science that are read, and xe is the number of pages of economics that are
read.
We know that Felicity can read 30 pages of political science per hour,
so it takes her 1/30 of an hour for each page. We know that Felicity
can read 5 pages of economics per hour, so it takes her 1/5 of an hour
for each page, and we know that she has only 10 hours available, t.
Therefore, the budget equation is (1/30)xs + (1/5)xe = 10.
If we set xs = 0, Felicity reads 300 pages of political science and if we
set xe = 0, Felicity reads 50 pages of economics. Here is a graph of
the budget constraint. The budget set is below this line.
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Felicity has another constraint. She is determined to complete at least30 pages of her economics reading. Therefore, we add a vertical lineat Economics = 30.

uploaded image

The shaded area is the budget set, the possibilities that are consistentwith the constraints.

Thanks