## [answered] Math 308 - Fall 2016 Programming Projects Instated of the p

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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 apunnen@sfu.ca

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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