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{MA162} \hfill {Project Description}  \\
{Spring 1999} 
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 In this project you will write a linear program, solve it using
LINDO and then examine whether the solution of the mathematical
problem is a reasonable solution to the problem that your linear
program claims to model.   The project will involve planning a diet by
a linear program. This is a convenient problem to study since all of
us have an opinion as to what is a good diet and the information
needed to write the linear program is easily available.



\hd{The project}  
Using the information attached to this handout, write a linear program
to determine the meal at McDonald's  which meets certain nutritional
requirements while minimizing the intake of fat or calories. 

To set up your linear programs, you will need to decide which food
items to include, which nutrients should be used as constraints and
what you should use as  your objective function.


After you formulate your linear program, type it into LINDO and solve
it. Examine LINDO's solution and consider the following questions.  Is
it a reasonable meal?  Why or why 
not? Can you give additional restrictions on your diet that were not
incorporated into your linear program?  Can you formulate these new
restrictions as linear inequalities?
After considering the above questions revise your linear 
program.  Did the changes you made have the expected effect?  Is the
solution more realistic?  
This process of solution and revision could probably be continued
without end.  However, your time is limited and your instructor's due
date is inflexible. Thus you should stop after one revision.

\hd{Structure} I ask that you work in groups of between 2 and 5 on
this project.  I expect that your report will consist of 2 to 7
handwritten pages and a few pages of LINDO printout.

Your report should outline the assumptions that go into the
formulation of your original linear program,   problems identified
after examining your first solution and what you did to correct these
problems.  Your report should be self contained description of your
work rather than a list of questions and answers.  Be sure that your
report clearly identifies the problems you find in your first linear
program and how you attempt to correct these problems.

If you want to use the dual prices from LINDO in your discussion, you
should note that in a minimization problem, the dual prices represent
decrease in objective function divided by increase in right hand side.
Thus the dual prices in a minimization problem will usually  be negative.  


\hd{Grading} You will be graded on 1) writing and clarity of
presentation, 2) correct and reasonable formulation of the linear
program   3) creativity.  
All members of a group will receive the same grade.  

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