HP 100 MATLAB: PSE # 1 College Cost-Benefit Analysis

HP 100 MATLAB: PSE # 1
College Cost-Benefit Analysis
Due September 24th, 2014
Problem Solving Exercises (PSEs) are designed to give you experience in writing
an actual program to solve an actual (simplified) real world problem. They help students
learn to think critically and work through the problem solving process. As such, do not
expect us to tell you how to solve the problem. We will give you the necessary tools;
however, how you go about solving it is up to you (and indeed, there are always multiple
ways to solve this kind of problem). They have also been, in previous years, one of the
most educationally rewarding parts of the course, according to students. Below, we frame
the problem you are to tackle.
You work for a small government sponsored research team, which has been
assigned to model a cost-benefit analysis for college students and graduates. The purpose
of this project is to determine the necessity and legitimacy of a bill proposed in congress.
This bill would increase financial aid for students attending more expensive universities,
based on the assumption that a better college name will result in higher post-graduation
earnings. The committee examining the bill wonders if the added expenses incurred by
students who choose to attend expensive private universities are worth the increased
standard of living they obtain upon graduation. The rest of your team has done work
modeling various colleges’ tuition and average graduate salary in order to provide you
with the data necessary to analyze this problem.
In order to model the increase in tuition over time for each university you will need the
tuition model developed by your team:
T = the cost of tuition, in dollars.
Co = the “pre-exponential tuition factor” based on statistical data for school, in dollars.
k = the “tuition constant” which is a function of the school’s majors (science and
engineering majors require expensive laboratory and other equipment) as well as
economic and other conditions. k has units of years-1.
t = the year being evaluated.
Additionally, your team has developed a model for the average starting salary of
graduates, based on tuition the year they graduated:
S = the average starting salary of graduates, in dollars.
g = the “graduation factor” which is based on school, similar to k, in dollars.
r = the “return constant” based on school, with units of dollars.
For the purposes of this study, four schools have been selected. All four are based in New
York, in an attempt to mitigate the influence of geographic conditions. Two technical
schools, Clarkson University and SUNY Stony Brook, are selected. Additionally, two
schools offering a wide range of majors including liberal arts, St. Lawrence and SUNY
Potsdam, are selected. Clarkson and St. Lawrence represent the high end of the tuition
spectrum while the two SUNY schools are less expensive. The following parameters are
to be used in your models for each school:
School
Clarkson
St. Lawrence
Potsdam
Stony Brook
Co
21,000
34,000
15,000
11,000
k
0.015
0.009
0.008
0.014
g
3,400
3,200
2,100
2,800
r
36,000
48,000
19,000
18,000
Because the bill being proposed is a long term program, the committee would like you to
examine the time frame of 2000 to 2060 for both tuition costs and expected salaries of
graduates. They are also interested in which school is most economically efficient for
students.
MATLAB Requirements:
 You are to solve the above problem using MATLAB. You will be asked to submit
your published code.
 Be sure to include adequate commenting and blank space.
 Be sure to display your results appropriately, not just leave off semi-colons.
 Make sure that the code can run for a variety of schools, not just the specified
ones presented here. This means using the input command for the various
constants.
 Create a plot of tuition for each school over the time frame and put your four plots
in the same window using subplots.
 Create a plot of the expected starting salary for graduates over the time frame and
put your four plots in the same window using subplots.
 Create a plot of the ratio of starting salary to tuition over the time frame for each
of the four schools. Graph all four curves in the same plot (no subplots).
 Report the school with the best salary/tuition ratio in 2011, as well as the value.
Place a star on the ratio plot at this point.
 Do not use loops. Doing so will result in a 10% reduction in grade.
 Submit a two page report (Technical Memo) which details your process,
assumptions, results and recommendations for the committee. Please note that we
are looking for a thoughtful report. Describe why you think certain school(s) are
better (not just by straight numbers – interpret them) as well as why you think the
committee should recommend or not recommend the bill. Think outside the box,
but remain professional, realistic and concise.
 Late submissions will NOT be accepted.