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Math 308 ? Fall 2016 Programming Projects
Instated of the project on the diet problem, you may choose to do a programming project in python.
Make sure you write in Python 3.x (not python 2.7). If you complete a very basic working program you
will earn 10 out of 15. The additional 5 points is for creativity. For example, good user interface,
additional features, flexibility etc. Deliverables include source code, and one example, along with
writeup of user?s manual. You can submit the final product electronically at email@example.com
Choose any one of the following projects:
1. Write a code for the simplex algorithm. You can assume that the problem is maximization with
less than or equal to constraints and the RHS is non-negative. The input is integer in the form of
vector c, vector b, matrix A. All variables are non-negative. All arithmetic operations must be
done representing numbers as fractions. You will need to define addition, subtraction, division,
multiplication functions with input is given as numerator/denominator form and modify the
pivot formula assuming all numbers as fractions. Print the tableau in each iteration. When
printing, if the denominator is 1, then it is printed as an integer otherwise as a fraction. Should
not use floating point arithmetic.
2. Write a code for the parametric simplex algorithm for parametric cost as well as parametric RHS
problems. You can assume that the problem is maximization with less than or equal to
constraints and the RHS is non-negative. The input is integer in the form of vector c, c*, vector b,
b*, matrix A. All variables are non-negative. You may use floating point arithmetic.
3. Develop a code for the lights out game discussed in class. One should be able to play the game
using your board. You may use pygame package. Consider the following variations as well. (1)
The starting board may have some cells already in light-out state. (2) Consider a different
lighting rule. For example, pressing a cell will light the cell as well as the cells diagonally
adjacent. Write also, an integer program for these new versions. You may use a 5 by 5 board. All
three versions (original and the new ones) should be usable.
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