Two Phase Simplex tableau method for the linear programming model
The first line of input will contain a string 'MAX' or 'MIN' followed by the number of constraints N. The next line will contain the coefficients for the objective function. The next N lines will contain the coefficients ai1 , ai2 , ..., for the i th constraint.
Note that this method assumes that all the constraints are of '<=' form. So, if a constraint is of '>=' form, convert it to '<=' form by changing the sign of the constraint. This doesn't affect the optimal point or the optimal value. For example:
'x1 + 2x2 >= 14' is equivalent to '-x1 - 2x2 <= -14'
python simplex_2Ph.py
Below is a list of examples and the corresponding input to the code:
===================
1. Maximize:
20x1 + 10x2
s.t:
x1 - x2 <= 1
3x1 + x2 <= 7
Input:
MAX 2
20 10
1 -1 1
3 1 7
===================
2. Maximize:
3x1 + 4x2
s.t:
2x1 + x2 <= 600
x1 + x2 <= 225
5x1 + 4x2 <= 1000
x1 + 2x2 >= 150
Input:
MAX 4
3 4
2 1 600
1 1 225
5 4 1000
-1 -2 -150
===================
3. Minimize:
x - x2
s.t:
x1 + x2 >= 2
-x1 + x2 >= 1
x2 <= 3
Input:
MIN 3
1 -2
-1 -1 -2
1 -1 -1
0 1 3
===================
4. Minimize:
2x1 + 3x2
s.t:
4x1 + 2x2 >= 12
x1 + 4x2 >= 6
Input:
MIN 2
2 3
-4 -2 -12
-1 -4 -6
Irshad Ahmad Bhat
MS-CSE IIITH, Hyderabad
[email protected]
[email protected]
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